Answer:
y = ⅔x - 5
Step-by-step explanation:
The line that passes through (-3, -7) will have the same slope (m) as the line, 2x - 3y = 24. This is because if two lines that are parallel to each other would have the same slope.
Rewrite 2x - 3y = 24, in the slope-intercept form, y = mx + b.
Thus:
2x - 3y = 24, rewritten would give us y = ⅔x - 8.
The slope of the line, 2x - 3y = 24, is ⅔.
Thus, the slope of the line that is parallel to 2x - 3y = 24, is also ⅔.
To find the equation, substitute a = -3, b = -7, and m = ⅔ into y - b = m(x - a).
Thus:
y + 7 = ⅔(x + 3)
Rewrite to make the equation in slope-intercept form.
Thus:
y + 7 = ⅔(x + 3)
3(y + 7) = 2(x + 3) ---› multiplication property of equality
3y + 21 = 2x + 6 ----› distributive property
3y = 2x + 6 - 21 ----› subtraction property of equality
3y = 2x - 15
y = ⅔x - 5 (division property of equality)
