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

Answer:

y = 3x + 5        

Step-by-step explanation:

1) First, find the slope between the pair of points. Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of points A and B into the formula and simplify:

$m = \frac{(-10)-(5)}{(-5)-(0)} \\m = \frac{-10-5}{-5-0} \\m = \frac{-15}{-5} \\m = 3$

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:

$y = 3x + 5$