Question

Write an equation in slope-intercept form for the line described.x-intercept (-7,0), y-intercept (0,1)

Answer 1

The points are

`(-7,0)\text{ and (0,1)}`

The equation is writing using the formula below

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_(2-)x_1)_{}`

where

`x_2=0,x_1=-7,y_2=1,y_1=0`

Then, we substitute the parameters into the formula above

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_(2-)x_1)_{} \\ (y-1)/(x-(-7))=(1-0)/(0-(-7)) \end{gathered}`

Simplifying further, we have

`\begin{gathered} (y-1)/(x+7)=(1)/(7) \\ 7(y-1)=x+7 \\ 7y-7=x+7 \\ 7y-x-14=0 \\ 7y=x+14 \end{gathered}`

Then in the slope-intercept form, we have the equation as

`y=(1)/(7)x+2`

Therefore the equation of the line in the slope-intercept form is

y=(1/7)x +2