The point-slope equation of the line that passes through point (-3, 1) is: [tex](y-1) = \frac{3}{2} (x + 3)[/tex]
The graph related to the question is attached below.
Recall:
Lines that are parallel to each other have the same slope value.
Find the slope (m) of the given line shown on the graph
Use the two points, (2, 2) and (-2, -4) to find the slope of the given line.
[tex]slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let,
[tex](2,2) = (x_1,y_1)\\(-2, -4) = (x_2, y_2)[/tex]
Plug in the values
[tex]slope (m) = \frac{-4-2}{-2-2} \\= \frac{-6}{-4}\\slope(m) = \frac{3}{2}[/tex]
Thus, slope of the line that passes through (-3, 1) would also be [tex]\frac{3}{2}[/tex].
Equation of a line in point-slope form is:
[tex](y - b) = m(x - a)[/tex]
Where,
[tex]m = \frac{3}{2} \\a = -3\\b = 1[/tex]
Substitute:
[tex](y - 1) = \frac{3}{2} (x - (-3))\\(y-1) = \frac{3}{2} (x + 3)[/tex]
Therefore, the equation in point-slope form is: [tex](y-1) = \frac{3}{2} (x + 3)[/tex]
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