Answer:
The equation in the slope-intercept form will be:
[tex]y=2x+10[/tex]
Step-by-step explanation:
Given the points
Finding the slope between two points
[tex]\left(x_1,\:y_1\right)=\left(-3,\:4\right),\:\left(x_2,\:y_2\right)=\left(-4,\:2\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-4}{-4-\left(-3\right)}[/tex]
[tex]m=2[/tex]
As the point-slope form of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
putting the values m=2 and the point (-3, 4)
[tex]y-4=2\left(x-\left(-3\right)\right)[/tex]
[tex]y-4=2\left(x+3\right)[/tex]
Writing the equation in slope-intercept form
[tex]y=mx+b[/tex]
where m is the slope, and b is the y-intercept
so the equation becomes
[tex]y-4=2\left(x+3\right)[/tex]
add 4 to both sides
[tex]y-4+4=2\left(x+3\right)+4[/tex]
[tex]y=2x+10[/tex]
Therefore, the equation in the slope-intercept form will be:
[tex]y=2x+10[/tex]
