Question

Line 1 passes through the points A(-15,-8) and B(-3,0). Line 2 has

Answer 1

Answer:

The equation of line 3 is;

y = $\frac{2}{3} x$ + 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 = $\frac{0 - -8}{-3 - -15} = \frac{8}{12} = \frac{2}{3}$

Picking another point (x,y) on the line;

Slope = $\frac{y - 0}{x - -3} = \frac{2}{3}$

y = $\frac{2}{3} x$ + 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 = $\frac{5}{3} x$ + 6

Finally, the equation of line 2 is;

y = 1$\frac{2}{3} x$ + 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 $\frac{2}{3}$

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 = $\frac{2}{3} x$ + 6