Answer:
1
Step-by-step explanation:
For this question, your friend is the point-slope form.
Point-slope form = [tex]y-y_1 = m(x-x_1)[/tex]
The only variables you replace are m = slope, y1 = y of a given point, and x1 = x of a given point.
First, we need to find the slope that is perpendicular to the equation [tex]y=-\frac{3}{4}x+5[/tex]
An equation that is perpendicular to another equation have to be negative reciprocals (negative inverse) of each other.
If the slope is 3, then the negative reciprocal of 3 is [tex]-\frac{1}{3}[/tex].
So, since the given slope is -3/4, the negative reciprocal is [tex]\frac{4}{3}[/tex].
We will use the negative reciprocal as m since we are trying to find the equation of line that includes (-3, -3) and is perpendicular to the other equation.
We will use point slope form using the (-3, -3) points and negative reciprocal as m.
[tex]y-y_1 = m(x-x_1)\\y-(-3) = \frac{4}{3} (x-(-3))\\y+3=\frac{4}{3}(x+3)[/tex]
Now, we need to convert this into slope-intercept form. The reason why we need to do this is because y = mx + b, where b is the y-intercept. To do this, solve for y - or in other words, isolate y..
[tex]y+3=\frac{4}{3}(x+3)\\y+3=\frac{4x}{3}+4\\y+3-3=\frac{4x}{3}+4-3\\y=\frac{4}{3}x+1[/tex]
The y-intercept of the line is 1.
