Question

write the slope intercept equation. the graph of f passes through (-6,4) and is perpendicular to the line that has an x-intercept of 2 and a y intercept of -6​

Answer 1

Answer:

y = $-\frac{1}{3} x$ + 2

Step-by-step explanation:

The slope of the line that has an x intercept of (2,0) and y-intercept of (0,-6) is:

Slope(s) = Change in y ÷ change in x

s = $\frac{0 - -6}{2 - 0}$ = 3

The slope of the perpendicular line to this line with slope of 3 has to have a slope of -1 ÷ 3 = $-\frac{1}{3}$

Reason: The product of slopes of lines perpendicular to each other have to be -1

So the slope of the perpendicular line that passes through (-6,4) is $-\frac{1}{3}$

As mentioned earlier, we derive a slope of a line by dividing the change in y by the change in x

Taking another point (x,y) on the line,

$-\frac{1}{3}$ = $\frac{y - 4}{x - -6}$

$-\frac{1}{3}$ = $\frac{y - 4}{x + 6}$

y - 4 = $-\frac{1}{3}$x - 2

y = $-\frac{1}{3}$x + 2