Question 588·Easy·Algebra

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A line passes through the points $(2,7)$ and $(6,15)$ in the $xy$ -plane. What is the slope of the line?

Your answer

Two points on a line cue the slope formula: change in $y$ divided by change in $x$ . Subtract coordinates in the same point order on top and bottom, then enter the fraction in Desmos. Reversing only one subtraction changes the sign, making a line that rises as $x$ increases appear to fall.

Hints

Hint 1
The slope tells you how much $y$ changes for each $1$ unit increase in $x$ . From the first point to the second, which $y$ -values should you subtract? Which $x$ -values belong underneath?
Hint 2
Use second point minus first for both changes. That keeps each $y$ -value paired with its $x$ -value. Put the $y$ change on top of the fraction, then let Desmos evaluate it.

Step-by-step

Find the change in $y$ per change in $x$
Step 1
Write the slope as a fraction
A slope is the change in $y$ divided by the matching change in $x$ . Moving from $(2,7)$ to $(6,15)$ , the $y$ change is $15-7$ and the $x$ change is $6-2$ . Keep the same point order in both subtractions: $m=\frac{15-7}{6-2}$ . Reversing only one subtraction would give the wrong sign.
Step 2
Evaluate the fraction
Type $\frac{15-7}{6-2}$ into Desmos. It prints $2$ , so $y$ rises by $2$ for each $1$ unit increase in $x$ . The line’s slope is $2$ . Grid in 2.

Lessons that teach this

SAT AlgebraBeginnerCoreFind slope and rate of change

Question 588·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this