Answer:
The equation of the line in point-slope will be:
[tex]y\:=\:\frac{1}{6}x-\frac{5}{3}[/tex]
Step-by-step explanation:
Given the points
Finding the slope between (4, -1) and (10, 0)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(4,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:0\right)[/tex]
[tex]m=\frac{0-\left(-1\right)}{10-4}[/tex]
[tex]m=\frac{1}{6}[/tex]
We know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Using the slope-intercept form to find the y-intercept 'b'
[tex]y = mx+b[/tex]
substituting m = 1/6 and the point (4, -1)
[tex]-1\:=\:\frac{1}{6}\left(4\right)+b[/tex]
[tex]\frac{2}{3}+b=-1[/tex]
subtract 2/3 from both sides
[tex]\frac{2}{3}+b-\frac{2}{3}=-1-\frac{2}{3}[/tex]
[tex]b=-\frac{5}{3}[/tex]
now substituting b = -5/3 and m = 1/6 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{1}{6}x+\left(-\frac{5}{3}\right)[/tex]
[tex]y\:=\:\frac{1}{6}x-\frac{5}{3}[/tex]
Therefore, the equation of the line in point-slope will be:
[tex]y\:=\:\frac{1}{6}x-\frac{5}{3}[/tex]
