Question

Write the equation of line AB in slope-intercept form, given the points A(0,5) and B(-5,-10) . In your final answer, include all of your calculations.

Answer 1

y = 3x + 5

Explanation:

1) First, find the slope between the pair of points. Use the slope formula
`m = (y_2-y_1)/(x_2-x_1)`. Substitute the x and y values of points A and B into the formula and simplify:

`m = ((-10)-(5))/((-5)-(0)) \\m = (-10-5)/(-5-0) \\m = (-15)/(-5) \\m = 3`

So, the slope is 3.

2) Now, identify the y-intercept of the line, or the point at which the line intersects the y-axis. All points on the y-axis have an x-value of 0. We're told that (0,5) is a point the line intersects, and since it has an x-value of 0, that must be the y-intercept.

3) Using slope-intercept format, represented by the equation
`y = mx + b`, write the equation of the line. Remember that the number in place of
`m`, or the coefficient of the x-term, is the slope. So, substitute 3 for
`m`. Also, remember that
`b` represents the y-intercept of a line, so substitute 5 in its place, too. This gives the following answer:

`y = 3x + 5`