Answer:
[tex](0,13/3)[/tex]
Step-by-step explanation:
Since we know the slope and a point, we can use the point-slope form.
Recall that the point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Let m be 2/3 and let (-5,1) be x₁ and y₁. Therefore:
[tex]y-(1)=\frac{2}{3}(x-(-5))[/tex]
Simplify:
[tex]y-(1)=\frac{2}{3}(x+5)[/tex]
Distribute:
[tex]y-1=\frac{2}{3} x+\frac{10}{3}[/tex]
Add 1 to both sides. The left cancels. 1 is the same as 3/3:
[tex]y=\frac{2}{3} x+\frac{10}{3}+\frac{3}{3}\\[/tex]
Simplify:
[tex]y=\frac{2}{3}x+\frac{13}{3}[/tex]
This is in slope-intercept form. The coefficient is the slope and the y-intercept is the constant. Thus, the y-intercept is 13/3.
