Question

Write an equation that represents the line. Use exact numbers?

Answer 1

Answer:

$\text{point-slope form}\\\huge\boxed{y+3=\dfrac{7}{5}(x+7)}$

$\text{slope-intercept form}\\\huge\boxed{y=\dfrac{7}{5}x+\dfrac{34}{5}}$

$\text{standard form}\\\huge\boxed{7x-5y=-34}$

$\text{general form}\\\huge\boxed{7x-5y+34=0}$

Step-by-step explanation:

The slope-point form of an equation of a line:

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

where

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

From the graph we have two points (-7, -3) and (-2, 4).

Substitute:

$m=\dfrac{4-(-3)}{-2-(-7)}=\dfrac{4+3}{-2+7}=\dfrac{7}{5}\\\\y-(-3)=\dfrac{7}{5}(x-(-7))\\\\y+3=\dfrac{7}{5}(x+7)$

Convert to the slope-intercept form (y = mx + b):

$y+3=\dfrac{7}{5}(x+7)\qquad|\text{use the distributive property}\\\\y+3=\dfrac{7}{5}x+\dfrac{49}{5}\qquad|\text{subtract}\ 3=\dfrac{15}{5}\ \text{from both sides}\\\\y=\dfrac{7}{5}x+\dfrac{34}{5}$

Convert to the standard form (Ax + By = C):

$y=\dfrac{7}{5}x+\dfrac{34}{5}\qquad|\text{multiply both sides by 5}\\\\5y=7x+34\qquad\text{subtract}\ 7x\ \text{from both sides}\\\\-7x+5y=34\qquad|\text{change the signs}\\\\7x-5y=-34$

Convert to the general form (Ax + By + C = 0):

$7x-5y=-34\qquad|\text{add 34 to both sides}\\\\7x-5y+34=0$