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Digital SAT · Solve it in Desmos

How to Solve Slope of a Line on Desmos (Digital SAT)

Reading m from slope-intercept form is instant, so lean on Desmos mainly to plot two points or a messy form and read the slope off the picture, which catches sign and order errors.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for slope of a line

The Desmos steps

  1. 1

    Graph it

    Type the equation, or plot the two points, in Desmos.

  2. 2

    Read the steepness

    Click two lattice points and read rise over run.

  3. 3

    Confirm

    Match that rise over run to your value, sign and all.

Worked in Desmos

Easy example
The equation of a line in the xy-plane is y=4x−9y = 4x - 9. What is the slope of this line?
A
−9-9
B
−4-4
44
D
99

A: Incorrect. This is the y-intercept, not the slope.

B: Incorrect. This has the wrong sign for the slope.

C: Correct. In y=mx+by = mx + b, the slope is the coefficient of xx, which is 4.

D: Incorrect. This uses the size of the intercept instead of the slope.

Explanation

The equation is in the form y=mx+by = mx + b, so the slope is the coefficient of xx: 4.

Medium example
A car's distance from a city is modeled by d=240−50td = 240 - 50t, where dd is in miles and tt in hours. What is the slope of this line?
A
−240-240
−50-50
C
5050
D
240240

A: Incorrect. This is the negative of the starting distance, not the slope.

B: Correct. In d=240−50td = 240 - 50t, the coefficient of tt is −50-50.

C: Incorrect. This drops the negative sign of the slope.

D: Incorrect. This is the starting distance, not the slope.

Explanation

The equation is in slope-intercept form with tt as the variable, so the slope is the coefficient of tt: −50-50.

Hard example
A line in the xy-plane is described by y+1=−4(x−3)y + 1 = -4(x - 3). What is the slope of the line?
-4
B
−14-\frac{1}{4}
C
14\frac{1}{4}
D
4

A: The slope is -4.

B: This inverts the slope (run over rise instead of rise over run).

C: This is the slope of a perpendicular line (negative reciprocal), not this line.

D: This flips the sign of the slope.

Explanation

In point-slope form y−y1=m(x−x1)y - y_1 = m(x - x_1), the slope mm is −4-4.

Detailed explanation

The form y+1=−4(x−3)y + 1 = -4(x - 3) is point-slope, where the factor multiplying the xx group is the slope. That factor is −4-4, so the slope is −4-4.

Try it with the calculator

Question 1easy

A line passes through the points (2,3)(2, 3) and (6,11)(6, 11) in the xy-plane. What is the slope of the line?

Question 2easy

The equation of a line in the xy-plane is y=−23x+5y = -\frac{2}{3}x + 5. What is the slope of this line?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve slope of a line questions on the SAT?

Reading m from slope-intercept form is instant, so lean on Desmos mainly to plot two points or a messy form and read the slope off the picture, which catches sign and order errors.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master slope of a line, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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