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Slope-Intercept Form Practice Problems

Fourteen hand-built problems on slope-intercept form, each fully worked. They cover reading m and b straight off an equation, the rearranging that has to happen first when y is not alone, building the equation from a point and a slope, and reading the two numbers as a rate and a starting value in a word problem.

  1. 1.

    State the slope of \(y = -5x + 2\).

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    The coefficient of \(x\) is the slope, so \(m = -5\).

  2. 2.

    State the \(y\)-intercept of \(y = -5x + 2\). Give the \(y\)-value.

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    The constant term, so the intercept is \((0,\ 2)\).

  3. 3.

    State the slope of \(y = 8 - \dfrac{1}{4}x\).

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    Reorder to \(y = -\dfrac{1}{4}x + 8\). The slope is \(-\dfrac{1}{4}\), not \(8\) — the slope is whatever multiplies \(x\).

  4. 4.

    Rearrange \(2x + 5y = 20\) into slope-intercept form. Give only the right-hand side.

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    \(5y = -2x + 20\), then divide every term by 5: \(y = -\dfrac{2}{5}x + 4\).

  5. 5.

    Rearrange \(6x - 3y = 9\) into slope-intercept form. Give only the right-hand side.

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    \(-3y = -6x + 9\), then divide by \(-3\): \(y = 2x - 3\). Dividing by a negative flips both signs.

  6. 6.

    Rearrange \(4x - 3y = 12\) into slope-intercept form. Give only the right-hand side.

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    \(-3y = -4x + 12\), so \(y = \dfrac{4}{3}x - 4\).

  7. 7.

    A line has slope \(4\) and passes through \((1,\ 6)\). Find \(b\).

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    Substitute into \(y = 4x + b\): \(6 = 4(1) + b\), so \(b = 2\) and the line is \(y = 4x + 2\).

  8. 8.

    A line has slope \(-3\) and passes through \((2,\ 1)\). Write it in slope-intercept form, giving only the right-hand side.

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    \(1 = -3(2) + b\) gives \(1 = -6 + b\), so \(b = 7\) and \(y = -3x + 7\).

  9. 9.

    Write the line through \((0,\ 4)\) and \((3,\ -2)\) in slope-intercept form, giving only the right-hand side.

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    One point is already the intercept, so \(b = 4\). The slope is \(\dfrac{-2 - 4}{3 - 0} = -2\), giving \(y = -2x + 4\).

  10. 10.

    Is the point \((3,\ -1)\) on the line \(y = -2x + 5\)? Answer yes or no.

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    Substitute: \(-2(3) + 5 = -1\), which matches the \(y\)-coordinate. Yes, the point is on the line.

  11. 11.

    Convert \(y - 4 = 3(x + 2)\) to slope-intercept form. Give only the right-hand side.

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    Expand: \(y - 4 = 3x + 6\), so \(y = 3x + 10\).

  12. 12.

    A phone plan costs \(\$15\) a month plus \(\$4\) per gigabyte. What does 6 GB cost, in dollars?

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    \(C = 4g + 15\), so \(C(6) = 24 + 15 = \$39\). The slope is the per-gigabyte rate and the intercept is the fixed monthly charge.

  13. 13.

    A car worth \(\$18{,}000\) loses \(\$2{,}000\) a year. After how many years is it worth nothing?

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    \(V = -2000t + 18000\). Setting \(V = 0\) gives \(2000t = 18000\), so \(t = 9\) years. That is the \(x\)-intercept of the model.

  14. 14.

    Are \(y = \dfrac{1}{2}x + 1\) and \(2y - x = 8\) parallel? Answer yes or no.

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    The second rearranges to \(2y = x + 8\), so \(y = \dfrac{1}{2}x + 4\). Same slope \(\dfrac{1}{2}\), different intercepts — parallel.
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Slope-Intercept Form Practice Problems

The Slope-Intercept Form lesson explains what each number controls and how to graph from them; this set is fourteen problems to practise on, each fully solved.

How to use this set

Half of these are reading problems and half are rearranging problems, and the order matters: solve for before you read anything off. Once is alone, the slope is the coefficient of and the intercept is the constant.

Where a problem asks for the equation, give only the right-hand side — 2x - 3. Where it asks for a single value or a yes/no, type just that.

Common mistakes to watch for

Reading the constant as the slope. In the slope is .

Dividing only one term. Going from to forgets the constant; it is .

Losing a sign when the -coefficient is negative. Dividing by changes every sign on the right.

Reading slope from standard form directly. Rearrange first, or use .

Where to go next

Point-Slope Form is the faster route when you have a point rather than an intercept, Standard Form is the third form, and Parallel and Perpendicular Lines puts the slope comparison to work.

Frequently Asked Questions

What are m and b in y = mx + b?+

is the slope, the coefficient of . is the -intercept, the constant, giving the point .

Why do I have to solve for y first?+

Because the slope is only visible once is alone. has slope , not — reading it before rearranging gives the wrong sign.

What happens when I divide by a negative?+

Every sign on the right flips. becomes . Missing that is the most common source of a wrong graph on this topic.

How do I find b if I have a point and a slope?+

Substitute the point's coordinates into and solve for . Point-slope form gets there in one step if you prefer.

What do m and b mean in a word problem?+

is a rate of change — price per unit, speed, depreciation per year. is the starting value when the input is zero — a fixed fee, an opening balance, an original price.

Which lines cannot be written this way?+

Vertical lines. They have undefined slope, so no value of works. Write them as .

More practice problems

Slope Practice Problems Point-Slope Form Practice Problems Standard Form of a Line Practice Problems