Question

Write an equation of the line in slope-intercept form and standard form

Answer 1

Given:

The graph of a line.

To find:

The equation of the line in slope-intercept form and standard form.

Solution:

From the given graph it is clear that the line passes through the points (0,-3) and (4,0). So, the slope of the line is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{0-(-3)}{4-0}$

$m=\dfrac{3}{4}$

The slope intercept form of a line is:

$y=mx+b$

Where, m is the slope and b is the y-intercept.

The y-intercept of the given line is -3 and the slope is $\dfrac{3}{4}$. So, the slope intercept form of the line is:

$y=\dfrac{3}{4}x+(-3)$

$y=\dfrac{3}{4}x-3$             ...(i)

Standard form of a line is:

$Ax+By=C$

Multiply both sides by 4 in (i).

$4y=3x-12$

$12=3x-4y$

$3x-4y=12$

Therefore, the slope intercept form of the line is $y=\dfrac{3}{4}x-3$ and the standard form of the line is $3x-4y=12$.