Answer:
The equation of line 3 is;
y = [tex]\frac{2}{3} x[/tex] + 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.
Equation of line 1:
Slope = change in y-axis ÷ change in x-axis
The slope of line 1 = [tex]\frac{0 - -8}{-3 - -15} = \frac{8}{12} = \frac{2}{3}[/tex]
Picking another point (x,y) on the line;
Slope = [tex]\frac{y - 0}{x - -3} = \frac{2}{3}[/tex]
y = [tex]\frac{2}{3} x[/tex] + 2 (this is the equation of line 1)
Equation of line 2:
We put the equation given, of line 2, in the cartesian plane format;
3y = 5x + 18
y = [tex]\frac{5}{3} x[/tex] + 6
Finally, the equation of line 2 is;
y = 1[tex]\frac{2}{3} x[/tex] + 6
Equation of line 3:
Given: Line 3 is parallel to line 1
The slopes of two parallel lines are the same so line 3 has a slope of [tex]\frac{2}{3}[/tex]
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 = [tex]\frac{2}{3} x[/tex] + 6
