The slope of a line is the change in the y values over the corresponding x values.
The value of x, that makes the points a linear function is -16/3
Given that:
[tex]m = 3[/tex]
[tex](x_1,y_1) = (x,2)[/tex]
[tex](x_2,y_2) = (-4,6)[/tex]
The slope (m) of a line is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]3 = \frac{6-2}{-4-x}[/tex]
[tex]3 = \frac{4}{-4-x}[/tex]
Cross multiply
[tex]3 \times (-4 -x) = 4[/tex]
Divide by 3
[tex]-4 -x = \frac 43[/tex]
Add 4 to both sides
[tex]-x = \frac 43 + 4[/tex]
Take LCM
[tex]-x = \frac{4 + 12}3[/tex]
[tex]-x = \frac{16}3[/tex]
Divide by -1
[tex]x =-\frac{16}3[/tex]
Hence, the value of x is -16/3
Read more about slopes at:
https://brainly.com/question/3605446
