Respuesta :
Solution
These two points, (-2, 2) and (-10,5).
[tex]\begin{gathered} (x_{1\text{ , }}y_1)\text{ = ( -2, 2)} \\ (x_2,y_2)\text{ = (-10,5)} \\ M\text{ =}\frac{y_2-y_1}{x_2-x_1} \\ M=\text{ }\frac{5-2}{-10-(-2)} \\ M=\text{ }\frac{3}{-10+2} \\ M=\frac{3}{-8} \end{gathered}[/tex]Part A
An equation for this line in point-slope form.
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ \\ y-2=-\frac{3}{8}(x-(-2) \\ y-2=-\frac{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}[/tex]Part B
This line in slope-intercept form
[tex]\begin{gathered} 8y\text{ + 3x=10} \\ \\ \text{make y the subject formula} \\ 8y=-3x+10 \\ \text{Divide both sides by 8} \\ y=\frac{-3x+10}{8} \\ y=\frac{-3x}{8}+\frac{10}{8} \\ y=\text{ }\frac{-3x}{8}+\text{ 1.25} \end{gathered}[/tex]Part C
If the y-coordinate of a point on this line is 7
[tex]\begin{gathered} y=\text{ }\frac{-3x}{8}+\text{ 1.2}5 \\ \text{when y=7 } \\ \text{substitute for y} \\ 7=\text{ }\frac{-3x}{8}+\text{ 1.2}5 \\ \text{collect the like terms} \\ 7-1.25\text{ =}\frac{-3x}{8} \\ 5.75=\frac{-3x}{8} \\ \text{cross multiply} \\ 46=-3x \\ \text{Divide both sides by -3} \\ x=-\frac{46}{3} \\ x=\text{ -15.3333} \end{gathered}[/tex]
