Question

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

Answer 1

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

`\text{slope-intercept form}\\\huge\boxed{y=(7)/(5)x+(34)/(5)}`

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

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

Explanation:

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

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

where

`m=(y_2-y_1)/(x_2-x_1)`

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

Substitute:

`m=(4-(-3))/(-2-(-7))=(4+3)/(-2+7)=(7)/(5)\\\\y-(-3)=(7)/(5)(x-(-7))\\\\y+3=(7)/(5)(x+7)`

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

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

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

`y=(7)/(5)x+(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`