Respuesta :
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
For lines to be perpendicular, their slopes have to be negative reciprocals of each other. (flip the sign +/- and the fraction(switch the numerator and the denominator))
For example:
Slope = 2 or [tex]\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]-\frac{1}{2}[/tex] (flip the sign from + to -, and flip the fraction)
Slope = [tex]-\frac{2}{5}[/tex]
Perpendicular line's slope = [tex]\frac{5}{2}[/tex] (flip the sign from - to +, and flip the fraction)
y = -2x + 4 The slope is -2, so the perpendicular line's slope is [tex]\frac{1}{2}[/tex]
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
[tex]y=\frac{1}{2} x+b[/tex] Since they gave you the point (0, 3), which is the y-intercept, you can just plug 3 into "b". Another way to find b is plugging in the point on the line (0, 3) into the equation, then isolate/get the variable "b" by itself
[tex]3=\frac{1}{2}(0)+b[/tex]
3 = b
[tex]y=\frac{1}{2} x+3[/tex]
