Answer:
An equation in the slope-intercept form will be:
[tex]y=-\frac{1}{2}x+0[/tex]
Step-by-step explanation:
Given the points
Finding the slope between the points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(4,\:-2\right),\:\left(x_2,\:y_2\right)=\left(2,\:-1\right)[/tex]
[tex]m=-\frac{1}{2}[/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.
substituting the values m=-1/2 and the point (4, -2) to determine the y-intercept i.e. 'b'.
[tex]y=mx+b[/tex]
[tex]-2=-\frac{1}{2}\left(4\right)+b[/tex]
[tex]\frac{1}{2}\cdot \:4+b=-2[/tex]
[tex]-2+b=-2[/tex]
[tex]b=0[/tex]
Now, substituting the values b=0 and m=-1/2 to determine the equation in the slope-intercept form.
[tex]y=mx+b[/tex]
[tex]y=-\frac{1}{2}x+0[/tex]
Thus, an equation in the slope-intercept form will be:
[tex]y=-\frac{1}{2}x+0[/tex]
