Answer:
The equation of line 3 is;
y =
+ 6
Step-by-step explanation:
Line 1 passes through the points A(-15,-8) andn B(-3,0)
Line 2 has equation shown below;
5x - 3y + 18 = 0
Line 3 is parallel to line 1 and has the same y-intercept as line 2.
We are to determine the equation of line 3.
<u>Equation of line 1:</u>
<u />
Slope = change in y-axis ÷ change in x-axis
The slope of line 1 = ![\frac{0 - -8}{-3 - -15} = \frac{8}{12} = \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B0%20-%20-8%7D%7B-3%20-%20-15%7D%20%20%3D%20%5Cfrac%7B8%7D%7B12%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
Picking another point (x,y) on the line;
Slope = ![\frac{y - 0}{x - -3} = \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7By%20-%200%7D%7Bx%20-%20-3%7D%20%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
y =
+ 2 (this is the equation of line 1)
<u>Equation of line 2:</u>
<u />
We put the equation given, of line 2, in the cartesian plane format;
3y = 5x + 18
y =
+ 6
Finally, the equation of line 2 is;
y = 1
+ 6
<u>Equation of line 3:</u>
<u />
Given: Line 3 is parallel to line 1
The slopes of two parallel lines are the same so line 3 has a slope of ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Given: Line 3 has the same y-intercept as line 2
The y-intecept of line 2 is 6 (y-intercept is the value of y when x = 0)
So the equation of line 3 is;
y =
+ 6