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
`(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
`(7)/(2)` and graph passes through (5,-2), so the equation of line is

`y-(-2)=(7)/(2)(x-5)`

`y+2=(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.