Question

Math

Posted about 1 month ago

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Use the given conditions to write an equation for the line in slope-intercept form.
Passing through $(-5,1)$ and perpendicular to the line whose equation is $y=5 / 3 x+1$
Write an equation for the line in slope-intercept form.
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Answer from Sia

Posted about 1 month ago

Solution by Steps

step 1

To find the slope of the line perpendicular to $y = \frac{5}{3}x + 1$, we first identify the slope of the given line, which is $\frac{5}{3}$

step 2

The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the perpendicular line is $-\frac{3}{5}$

step 3

Now, we need to write the equation of a line with slope $-\frac{3}{5}$ passing through the point $(-5, 1)$. We use the point-slope form of the equation: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the point $(-5, 1)$ and $m$ is the slope $-\frac{3}{5}$

step 4

Substituting the values, we get: $y - 1 = -\frac{3}{5}(x + 5)$

step 5

Simplifying the equation: $y - 1 = -\frac{3}{5}x - 3$

step 6

Adding 1 to both sides to get the equation in slope-intercept form: $y = -\frac{3}{5}x - 2$

Answer

$y = -\frac{3}{5}x - 2$

Key Concept

Slope of perpendicular lines

Explanation

The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.

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