Respuesta :
We have the following two points that belong to a line:
[tex](6,r)\text{ and }(-22,15)[/tex]And also the slope of the line:
[tex]m=-\frac{3}{4}[/tex]And we have to find the missing coordinate r.
To find that, we can proceed as follows:
1. We can label both points as follows:
• (6, r) ---> x1 = 6, y1 = r
,• (-22, 15) ---> x2 = -22, y2 = 15
2. Now, we can use the formula for the slope of a line - since the slope of the line was given. Then we have:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=-\frac{3}{4} \end{gathered}[/tex]3. Then we can substitute the corresponding values into the above equation as follows:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}},m=-\frac{3}{4},x_1=6,y_1=r,x_2=-22,y_2=15 \\ \\ -\frac{3}{4}=\frac{15-r}{-22-6} \end{gathered}[/tex]4. And now, we have to solve the equation for r as follows:
[tex]\begin{gathered} -\frac{3}{4}=\frac{15-r}{-28} \\ \\ \text{ Multiply by -28 to both sides of the equation:} \\ \\ -28(-\frac{3}{4})=\frac{-28\left(15-r\right)}{-28} \\ \\ \frac{-28}{4}(-3)=\frac{28}{28}(15-r) \\ \\ -7(-3)=15-r \\ \\ 21=15-r \end{gathered}[/tex]5. Finally, we can subtract 15 from both sides of the equation:
[tex]\begin{gathered} -21-15=15-15-r \\ \\ -36=-r \\ \\ \text{ Then we have that \lparen we can multiply by -1 to both sides of the equation\rparen:} \\ \\ 36=r \\ \\ r=36 \end{gathered}[/tex]