Question

6. A line goes through these two points, (-4, -1) anti (-9,-5).A. Find an equation for this line in point slope form.B. Find the equation for this line in slope intercept form. Be sure to show your work.C. If the y-coordinate of a point on this line is 7, what is the x-coordinate of this point?

Answer 1

A. In order to find the equation, first we need to find the slope

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

m is the slope

(-4, -1)=(x1,y1)

(-9,-5)=(x2,y2)

we substitute the values

`m=(-5+1)/(-9+4)=(-4)/(-5)=(4)/(5)`

then we use the point-slope form

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

we substitute the values

`y+1=(4)/(5)(x+4)`

B. in order to find the slope-intercept form we need to isolate the y

`y=(4)/(5)x+(11)/(5)`

C. if the y coordinate is 7

`7=(4)/(5)(x)+(11)/(5)`

then we isolate the x

`(4)/(5)x=7-(11)/(5)`
`\begin{gathered} (4)/(5)x=(24)/(5) \\ x=(5\cdot24)/(5\cdot4) \\ x=6 \end{gathered}`

the value of the x-coordinate is 6 when the y-coordinate is 7