Question

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Answer 1

Answer:

We conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:

$\:y=\frac{1}{2}x+\frac{13}{2}$

Step-by-step explanation:

Given the line

y+2x=4

converting into the slope-intercept form y = mx+b where m is the slope

y = -2x+4

comparing with the slope-intercept form

Thus, the slope is: m = -2

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -2

The slope of the new line perpendicular to the given line = – 1/m

                                                                                                = -1/-2 = 1/2

Using the point-slope form

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 1/2 and the point (-3, 5)

$y-y_1=m\left(x-x_1\right)$

$y-5=\frac{1}{2}\left(x-\left(-3\right)\right)$

$y-5=\frac{1}{2}\left(x+3\right)$

Add 5 to both sides

$y-5+5=\frac{1}{2}\left(x+3\right)+5$

$\:y=\frac{1}{2}x+\frac{13}{2}$

Therefore, we conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:

$\:y=\frac{1}{2}x+\frac{13}{2}$