an equation for a line that passes through (0,5) and (5,8)

Answer 1

You can write the equation with the slope and one point, or with the slope and the y-intercept.

One of the points is (0,5) which means it is on the y-axis (since x=0) so the y-intercept is 5.

Now you need the slope (y2-y1)/(x2-x1) = (8-5)/(5-0) = 3/5

Now use slope-intercept form: y = mx+b with m=3/5 and b=5

y=(3/5)x + 5