Question

Find an equation of the line containing the given pair of points in​ point-slope form and in​ slope-intercept form.

Answer 1

Answer:

Part 1) $y-5=\frac{1}{2}(x-1)$

Part 2) $y=\frac{1}{2}x+\frac{9}{2}$  or $y=0.5x+4.5$

Step-by-step explanation:

we have

​(1​,5​) and ​(3​,6​)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{6-5}{3-1}$

$m=\frac{1}{2}$

Part 1) Find the equation in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{1}{2}$

$point\ (1,5)$

substitute

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

Part 2) Find the equation in slope-intercept form

$y=mx+b$

we have

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

isolate the variable y

$y-5=\frac{1}{2}x-\frac{1}{2}\\\\y=\frac{1}{2}x-\frac{1}{2}+5\\\\y=\frac{1}{2}x+\frac{9}{2}$