Question

14. A line goes through these two points, (-2, 2) and (-10,5).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

These two points, (-2, 2) and (-10,5).

`\begin{gathered} (x_{1\text{ , }}y_1)\text{ = ( -2, 2)} \\ (x_2,y_2)\text{ = (-10,5)} \\ M\text{ =}(y_2-y_1)/(x_2-x_1) \\ M=\text{ }(5-2)/(-10-(-2)) \\ M=\text{ }(3)/(-10+2) \\ M=(3)/(-8) \end{gathered}`

Part A

An equation for this line in point-slope form.

`\begin{gathered} y-y_1=m(x_{}-x_1) \\ \\ y-2=-(3)/(8)(x-(-2) \\ y-2=-(3)/(8)(x+2) \\ \text{clear the fraction by multiplying both sides by 8} \\ 8(y-2)=-3(x+2) \\ 8y-16=-3x-6 \\ \\ 8y+3x=10 \end{gathered}`

Part B

This line in slope-intercept form

`\begin{gathered} 8y\text{ + 3x=10} \\ \\ \text{make y the subject formula} \\ 8y=-3x+10 \\ \text{Divide both sides by 8} \\ y=(-3x+10)/(8) \\ y=(-3x)/(8)+(10)/(8) \\ y=\text{ }(-3x)/(8)+\text{ 1.25} \end{gathered}`

Part C

If the y-coordinate of a point on this line is 7

`\begin{gathered} y=\text{ }(-3x)/(8)+\text{ 1.2}5 \\ \text{when y=7 } \\ \text{substitute for y} \\ 7=\text{ }(-3x)/(8)+\text{ 1.2}5 \\ \text{collect the like terms} \\ 7-1.25\text{ =}(-3x)/(8) \\ 5.75=(-3x)/(8) \\ \text{cross multiply} \\ 46=-3x \\ \text{Divide both sides by -3} \\ x=-(46)/(3) \\ x=\text{ -15.3333} \end{gathered}`