Answer:
As a fraction: [tex]y=\frac{56}{5}[/tex]
As a decimal: [tex]y=11.2[/tex]
As an ordered pair: [tex](0,\frac{56}{5} )[/tex] or [tex](0,11.2)[/tex]
Step-by-step explanation:
First we are using the slope formula to find the equation of our line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
[tex]m[/tex] is the slope of the line
[tex](x_1,y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
our first point is (8, 0) and our second point is (3, 7), so [tex]x_1=8[/tex], [tex]y_1=0[/tex], [tex]x_2=3[/tex], and [tex]y_2=7[/tex].
Replacing values:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-0}{3-8}[/tex]
[tex]m=\frac{7}{-5}[/tex]
[tex]m=-\frac{7}{5}[/tex]
Now, to complete the equation of our line (and find its y-intercept), we are using the point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
Replacing values:
[tex]y-0=-\frac{7}{5} (x-8)[/tex]
[tex]y=-\frac{7}{5} x+\frac{56}{5}[/tex]
Now, in a line of the form [tex]y=mx+b[/tex], [tex]b[/tex] is the way intercept. We can infer form our line that [tex]b=\frac{56}{5}[/tex], so the y-intercept of the line joining the points (8, 0) and (3, 7) is [tex]\frac{56}{5}[/tex].
