Use the given conditions to write an equation for the line in slope-intercept form.
Passing through $(-5,3)$ and parallel to the line whose equation is $y=3 / 2 x+9 / 4$
Write an equation for the line in slope-intercept form.

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Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the slope of the given line. The given line is $y = \frac{3}{2}x + \frac{9}{4}$. The slope (m) is $\frac{3}{2}$. ‖ ‖ step 2 ⋮ Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also $\frac{3}{2}$. ‖ ‖ step 3 ⋮ Use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the point the line passes through. Here, $(x_1, y_1) = (-5, 3)$ and $m = \frac{3}{2}$. ‖ ‖ step 4 ⋮ Substitute the values into the point-slope form: $y - 3 = \frac{3}{2}(x - (-5))$. ‖ ‖ step 5 ⋮ Simplify the equation: $y - 3 = \frac{3}{2}(x + 5)$. ‖ ‖ step 6 ⋮ Distribute the slope: $y - 3 = \frac{3}{2}x + \frac{15}{2}$. ‖ ‖ step 7 ⋮ Add 3 to both sides to solve for $y$: $y = \frac{3}{2}x + \frac{15}{2} + 3$. ‖ ‖ step 8 ⋮ Convert 3 to a fraction with a common denominator: $3 = \frac{6}{2}$. ‖ ‖ step 9 ⋮ Combine the fractions: $y = \frac{3}{2}x + \frac{15}{2} + \frac{6}{2} = \frac{3}{2}x + \frac{21}{2}$. ‖ ∻Answer∻ ⚹ The equation of the line in slope-intercept form is $y = \frac{3}{2}x + \frac{21}{2}$. ⚹ ∻Key Concept∻ ⚹Parallel lines have the same slope.⚹ ∻Explanation∻ ⚹To find the equation of a line parallel to a given line, use the same slope and apply the point-slope form with the given point.⚹◊What is the formula for the slope-intercept form of a line?⍭ Generate me a similar question◊

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