Slope-intercept form is:
y = mx + b
"m" being the slope, "b" being the y-intercept(when x = 0)
You first isolate the "y" in the given equation.
y - 2 = 3(x + 7) Multiply the 3 into (x + 7)
y - 2 = 3x + 21 Add 2 on both sides to get "y" by itself
y = 3x + 23
For the equation of the line to be perpendicular to the given equation, the slope has to be the opposite(you flip the sign and the number of the given slope)
For example:
slope = -2
the perpendicular line's slope = 1/2(positive)
slope = 4/5
the perpendicular line's slope = -5/4(negative)
The given slope is 3 or [tex]\frac{3}{1}[/tex], when you flip the sign and the number, the perpendicular line's slope is [tex]-\frac{1}{3}[/tex]
[tex]y = -\frac{1}{3} x + b[/tex]
Now you need to find b, to do so you plug in the point (4,2) into the equation
[tex]y = -\frac{1}{3}x + b[/tex]
[tex]2 = -\frac{1}{3} (4) + b[/tex]
[tex]2 = -\frac{4}{3} + b[/tex] Add 4/3 on both sides
[tex]2 + \frac{4}{3} = b[/tex] Make the denominators the same
[tex]\frac{6}{3}+ \frac{4}{3} = b[/tex]
[tex]\frac{10}{3} = b[/tex]
Your equation is:
[tex]y = -\frac{1}{3} x + \frac{10}{3}[/tex]
