Answer:
The y-intercept is (0,-26)
Step-by-step explanation:
Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression
[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]
We'll take the first two points P(34,-52) and Q(51,-65) to find
[tex]y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26[/tex]
Let's verify if the third point is on the line:
[tex]y=-\frac{13}{17}68-26=-52-26=-78[/tex]
It belongs to the line. To find the y-intercept of the line, we set x to 0
[tex]y=-\frac{13}{17}(0)-26=-26[/tex]
The y-intercept is (0,-26)
