Question

Which equation in standard form has a graph that passes through the point (5, −2) and has a slope of 72 ?

A. 7x − 2y = 35
A. 7x − 2y = 35

B. 7x − 2y = 39
B. 7x − 2y = 39

C. 7x − 2y = −31
C. 7x − 2y = −31

D. 7x − 2y = −24
D. 7x − 2y = −24

Answer 1

Given:

Consider the graph passes through the point (5, −2) and has a slope of $\dfrac{7}{2}$.

To find:

The equation of graph in standard form.

Solution:

Point slope form of a line is

$y-y_1=m(x-x_1)$

where, m is slope and $(x_1,y_1)$ is the point lies on the line.

Slope is $\dfrac{7}{2}$ and graph passes through (5,-2), so the equation of line is

$y-(-2)=\dfrac{7}{2}(x-5)$

$y+2=\dfrac{7}{2}(x-5)$

Multiply both sides by 2.

$2(y+2)=7(x-5)$

$2y+4=7x-35$

$4+35=7x-2y$

$39=7x-2y$

The required equation is $7x-2y=39$.

Therefore, the correct option is B.