Question

What is the equation in slope intercept form of the line that passes through the points (-6,5) and (2,1) enter any fractions like a/b or -a/b. Do not use spaces in your answer

Answer 1

The equation of the line in slope-intercept form is given by

$y=mx+b$

step 1

Find out the slope m

we have the points (-6,5) and (2,1)

$m=\frac{1-5}{2+6}=-\frac{4}{8}=-\frac{1}{2}$

step 2

Find out the equation of the line

we have

m=-1/2

point (2,1)

substitute and solve for b

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

therefore

The equation of the line is

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

Problem N 2

Write the equation of the line in the point-slope form that passes through the point (-2,3) and has a slope of 1/2

The equation of the line in point-slope form is given by

$y-y_1=m(x-x_1)$

we have

m=1/2

point (-2,3)

substitute

$\begin{gathered} y-3=\frac{1}{2}(x-(-2)) \\ \\ therefore \\ The\text{ answer is} \\ y-3=\frac{1}{2}(x+2) \end{gathered}$