How do you write an equation in slope-intercept form for the line that passes through $(4,-2)$ and is parallel to the graph of $y=1/2x-7$ ?

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Answer 1 · 2016-11-19T22:59:02

$y=1/2 x -4$

Equation of line through $(4,-2)$ and parallel to $y=1/2 x-7$

The given equation is in the form $y=mx+b$ , where $m=$ slope.

Parallel lines have equal slopes, so the slope of the line we are trying to find is $m=1/2$ .

Next, use the point-slope form of a line:

$y-y_1=m(x-x_1)$ where $(x_1,y_1)$ is a point on the line.

$y- -2=1/2 (x-4)$

$y+2=1/2 x -2$
$color(white)a-2color(white)(aaaaaa)-2$

$y=1/2 x -4$

OR

Use the slope intercept form of a line (again with $m= 1/2$ ):

$y=mx+b$ where $b=$ the $y$ intercept.

Plug in $(4,-2)$ for $x and y$ and solve for $b$ .

$-2=1/2 (4)+b$

$-2=color(white)(aa^2)2+b$
$-2=-2$

$-4=b$

The equation is then $y= 1/2 x-4$

How do you write an equation in slope-intercept form for the line that passes through (4,-2)(4,-2) and is parallel to the graph of y=1/2x-7y=1/2x-7?