Question

Can you please help me solve this problem:Write an equation in slope intercept form, but if it can’t be written in that form write it in standard form.26. passes through the point (-2,3) and is parallel to the line 2x-4y = 10

Answer 1

step 1

Find out the slope of the given line

$\begin{gathered} 2x-4y=10 \\ isolate\text{ the variable y} \\ 4y=2x-10 \\ y=\frac{2}{4}x-\frac{10}{4} \\ simplify \\ y=\frac{1}{2}x-\frac{5}{2} \end{gathered}$

The slope of the given line is m=1/2

step 2

Remember that

If two lines are parallel, then their slopes are equal

that means

The slope of the line parallel to the given line is m=1/2 too

step 3

Find out the equation of the parallel line in slope-intercept form

$y=mx+b$

we have

m=1/2

point (-2,3)

substitute and solve for b

$\begin{gathered} 3=\frac{1}{2}(-2)+b \\ \\ 3=-1+b \\ b=4 \end{gathered}$

therefore

The equation of the line is

$y=\frac{1}{2}x+4$