Question

What is the equation of the line in point-slope form containing the points (4, -1) and (10, 0)?

Answer 1

Answer:

The equation of the line in point-slope will be:

$y\:=\:\frac{1}{6}x-\frac{5}{3}$

Step-by-step explanation:

Given the points

• (4, -1)

• (10, 0)

Finding the slope between  (4, -1) and (10, 0)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(4,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:0\right)$

$m=\frac{0-\left(-1\right)}{10-4}$

$m=\frac{1}{6}$

We know that the slope-intercept form of the line equation is

$y = mx+b$

where m is the slope and b is the y-intercept

Using the slope-intercept form to find the y-intercept 'b'

$y = mx+b$

substituting m = 1/6 and the point (4, -1)

$-1\:=\:\frac{1}{6}\left(4\right)+b$

$\frac{2}{3}+b=-1$

subtract 2/3 from both sides

$\frac{2}{3}+b-\frac{2}{3}=-1-\frac{2}{3}$

$b=-\frac{5}{3}$

now substituting b = -5/3 and m = 1/6 in the slope-intercept form

$y = mx+b$

$y\:=\:\frac{1}{6}x+\left(-\frac{5}{3}\right)$

$y\:=\:\frac{1}{6}x-\frac{5}{3}$

Therefore, the equation of the line in point-slope will be:

$y\:=\:\frac{1}{6}x-\frac{5}{3}$

Answer 2

Find slope first
(0+1)/(10-4)= 1/6
Point slope: (y-y1) = m(x-x1)
Solution: (y+1) = 1/6(x-4)