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Quizzes > High School Quizzes > Mathematics

Standard and Slope-Intercept Worksheet Practice Quiz

Ace Unit 2 Linear Functions with Guided Practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz on converting linear equation forms for high school students.

Convert the equation 2x + 3y = 6 to slope-intercept form.
y = (-2/3)x + 2
y = (2/3)x + 2
y = (-3/2)x + 2
y = 2x - 3
By isolating y in the equation 2x + 3y = 6 (subtract 2x from both sides and divide by 3), you obtain y = (-2/3)x + 2. This clearly shows the slope is -2/3 and the y-intercept is 2.
Identify the slope of the line represented by y = 5x - 7.
5
-7
-5
7
In the slope-intercept form y = mx + b, the coefficient of x directly represents the slope. Here, m is 5, making the slope 5.
What is the y-intercept of the line with equation y = -3x + 4?
4
-3
-4
3
In the form y = mx + b, the y-intercept is represented by b. Here, b is 4, which is the point where the line crosses the y-axis.
Which of the following forms correctly represents the slope-intercept form of a line?
y = mx + b
Ax + By = C
y - b = m(x - a)
b = y - mx
The slope-intercept form is defined as y = mx + b, where m is the slope and b is the y-intercept. The other options represent either the standard form or point-slope variations.
Which step is essential when converting from standard form Ax + By = C to slope-intercept form?
Subtract Ax from both sides and divide by B
Multiply the entire equation by A
Add B to both sides and then divide by A
Switch the positions of A and B
To convert to slope-intercept form, you must isolate y. This involves subtracting Ax from both sides and then dividing all terms by B to solve for y.
Convert the equation 4x - 2y = 8 to slope-intercept form.
y = 2x - 4
y = -2x + 4
y = -2x - 4
y = 2x + 4
Subtract 4x from both sides to get -2y = -4x + 8, then divide by -2 to isolate y, which results in y = 2x - 4.
Determine the slope of the line given by 3x + 6y = 12.
-1/2
1/2
3
-3
Rearrange the equation to slope-intercept form: 6y = -3x + 12 becomes y = (-1/2)x + 2. The coefficient of x, -1/2, is the slope.
Given the equation y = 7 - 3x, identify the slope and y-intercept.
Slope: -3, y-intercept: 7
Slope: 7, y-intercept: -3
Slope: 3, y-intercept: -7
Slope: -7, y-intercept: 3
The equation can be rewritten as y = -3x + 7, making it clear that the slope is -3 and the y-intercept is 7.
Transform the slope-intercept equation y = (1/2)x - 3 into standard form.
x - 2y = 6
2x - y = 6
2y - x = 6
2x + y = 6
Multiply the entire equation by 2 to eliminate the fraction, yielding x - 6 = 2y, and then rearrange to obtain the standard form: x - 2y = 6.
Express the line with slope -4 and y-intercept 1 in slope-intercept form.
y = -4x + 1
y = 4x + 1
y = -4x - 1
y = x - 4
Simply insert the given slope and y-intercept into the slope-intercept formula y = mx + b to get y = -4x + 1.
Convert the equation 5 - y = (3/2)x into slope-intercept form.
y = -(3/2)x + 5
y = (3/2)x - 5
y = -(2/3)x + 5
y = (2/3)x + 5
Rearrange the given equation by subtracting (3/2)x from 5 - y to isolate y, resulting in y = -(3/2)x + 5.
Find the standard form of the line that passes through the point (0, -2) with a slope of 3.
3x - y = 2
y = 3x - 2
3x + y = -2
-3x + y = 2
Start by forming the slope-intercept equation y = 3x - 2 using the given point and slope. Rearranging this equation yields the standard form 3x - y = 2.
What is the slope of the line represented in standard form by -2x + 5y = 10?
2/5
-2/5
5/2
-5/2
Rearrange the equation to solve for y: 5y = 2x + 10, so y = (2/5)x + 2. The coefficient (2/5) is therefore the slope.
Determine the equation of the line parallel to 4x - 7y = 14 that passes through (7, 0).
y = (4/7)x - 4
y = (7/4)x - 4
y = (4/7)x + 4
y = (7/4)x + 4
First, convert 4x - 7y = 14 to slope-intercept form to find its slope, which is 4/7. Then, using the point (7, 0) and the same slope in the point-slope formula produces y = (4/7)x - 4.
Rewrite the equation 0.5x + y = 3 in slope-intercept form.
y = -0.5x + 3
y = 0.5x + 3
y = 3x - 0.5
y = -3x + 0.5
Subtract 0.5x from both sides to isolate y and obtain y = -0.5x + 3, which is the slope-intercept form.
Given the standard form equation 2x + 3y = 6, determine the slope and y-intercept by converting it to slope-intercept form.
m = -2/3, y-intercept = 2
m = 2/3, y-intercept = 2
m = -2/3, y-intercept = -2
m = 3/2, y-intercept = 2
Converting 2x + 3y = 6 involves subtracting 2x and dividing by 3, which yields y = (-2/3)x + 2. Thus, the slope is -2/3 and the y-intercept is 2.
Convert the slope-intercept equation y = -1/4x + 7 to standard form.
x + 4y = 28
4x + y = 28
-x + 4y = 28
x - 4y = 28
Multiplying the equation y = -1/4x + 7 by 4 eliminates the fraction, yielding 4y = -x + 28, which can be rearranged to the standard form x + 4y = 28.
A line in standard form is given by -3x + 6y = 12. Convert it to slope-intercept form and identify its slope.
y = (1/2)x + 2, slope = 1/2
y = (1/2)x - 2, slope = 1/2
y = -(1/2)x + 2, slope = -1/2
y = -(1/2)x - 2, slope = -1/2
Solve for y by adding 3x to both sides and dividing by 6 to get y = (1/2)x + 2. The coefficient (1/2) is the slope.
A line is given in slope-intercept form as y = (5/3)x + k. If the line passes through (3, 8), find the value of k and write the equation in standard form.
k = 3; 5x - 3y = -9
k = 3; 5x - 3y = 9
k = -3; 5x + 3y = 9
k = -3; 3x + 5y = 9
By substituting (3, 8) into y = (5/3)x + k, you find k = 3. Clearing fractions from y = (5/3)x + 3 leads to the standard form 5x - 3y = -9.
Find the equation of the line that is perpendicular to 2x + 3y = 6 and passes through the x-intercept of this line.
y = (3/2)x - 9/2
y = (-3/2)x + 9/2
y = (2/3)x - 3
y = (-2/3)x - 3
First, find the x-intercept of 2x + 3y = 6 by setting y = 0, which gives x = 3. The slope of the given line is -2/3, so the perpendicular slope is 3/2. Using the point-slope formula with (3, 0) leads to y = (3/2)x - 9/2.
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Study Outcomes

  1. Analyze the structure of standard and slope-intercept forms.
  2. Convert equations from standard to slope-intercept form accurately.
  3. Apply algebraic manipulation to isolate variables and simplify expressions.
  4. Interpret the roles of slope and y-intercept in the context of a linear equation.
  5. Evaluate the correctness of conversions through targeted problem-solving.

Standard & Slope-Intercept Cheat Sheet

  1. Understand Standard Form - Standard Form is written as Ax + By = C, making it easy to spot coefficients and constants at a glance. This layout shines when you're analyzing linear relationships or tackling systems of equations. Ready to see it in action? Convert Slope to Standard Form
  2. Master Slope‑Intercept Form - In y = mx + b, "m" tells you the slope and "b" gives the y‑intercept right away, so it's perfect for quick graphing. You'll instantly know how steep the line is and where it crosses the y‑axis. It's your go‑to for visualizing behavior! Converting Between Standard & Slope‑Intercept Forms
  3. Convert Standard → Slope‑Intercept - Start by isolating y: move terms with x over to the other side, then divide by the coefficient on y. For example, 4x + 2y = 12 becomes y = - 2x + 6 in just two steps. Practice this move until it feels like second nature! Convert Standard to Slope‑Intercept
  4. Convert Slope‑Intercept → Standard - Multiply through to clear fractions and rearrange: transform y = (3/4)x - 2 into 3x - 4y = 8 in one smooth sweep. This back‑and‑forth fluency is a game changer when you switch between solving and graphing. Keep your algebra toolkit sharp! Slope‑Intercept to Standard Form
  5. Interpret the Slope (m) - The slope m measures how steep your line climbs or falls: positive m means an uphill ride, negative m takes you downhill. Steeper lines have bigger absolute values. Understanding this lets you predict trends at a glance! Slope & Graph Behavior
  6. Spot the Y‑Intercept (b) - In y = mx + b, b is the exact point where your line crosses the y‑axis - no extra work needed. This handy intercept tells you the starting value before any changes occur. Graphing becomes as simple as marking one point! Y‑Intercept Insights
  7. Use Point‑Slope Form - When you know one point (x₝, y₝) and the slope m, plug into y - y₝ = m(x - x₝) for lightning‑fast equation writing. It's perfect for "pointy" problems where you already have a coordinate pair. Write neat equations in just a couple of steps! Point‑Slope Form Guide
  8. Remember "SIR" - Slope‑Intercept form Is Ready for graphing: it shows both the slope (S) and the y‑intercept (I) right away. That R stands for "Ready to draw." Mnemonics like "SIR" make studying stick in your brain! SIR: Quick Graphing
  9. Practice with Interactive Tools - Dynamic widgets let you drag points, adjust slopes, and watch equations update in real time. Playing with these tools turns abstract concepts into hands‑on adventures. Give your skills a fun workout! GeoGebra Conversion Tool
  10. Apply to Real‑World Problems - Use linear equations to model everything from budgeting to predicting population growth. Seeing these formulas solve actual puzzles highlights their power. Real applications make studying way more exciting! Media4Math: Linear Functions in Action
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