Answer:
Step-by-step explanation:
(5 + 4)/(3 + 2) = 9/5
y - 5 = 9/5(x - 3)
y - 25/5 = 9/5x - 27/5
y = 9/5x - 2/5
The equation of the line parallel to the points (-2, -4) and (3, 5) is [tex]y = \frac{9}{5}x-\frac{2}{5}[/tex]
The line passes through the points (-2, -4) and (3, 5)
That is, x₁ = -2, y₁ = -4, x₂ = 3, y₂ = 5
The slope(m) of the line is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{5-(-4)}{3-(-2)} \\\\m = \frac{5+4}{3+2} \\\\m = \frac{9}{5}[/tex]
The equation parallel to the line will be given as:
[tex]y - y_1 = m(x - x_1)\\\\y - (-4) = \frac{9}{5}(x -(-2))\\\\y + 4 = \frac{9}{5}(x + 2)\\\\y+4 = \frac{9}{5}x + \frac{18}{5}\\\\y = \frac{9}{5}x+\frac{18}{5} - 4\\\\y = \frac{9}{5}x-\frac{2}{5}[/tex]
The equation of the line parallel to the points (-2, -4) and (3, 5) is [tex]y = \frac{9}{5}x-\frac{2}{5}[/tex]
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