Question

Math

Posted about 2 months ago

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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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Answer from Sia

Posted about 2 months ago

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.

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