Question

Write the equation of the line in slope-intercept form that goes through the points: (0, 3) and (3, -6)

Answer 1

Answer:

y = -3x + 3  

Step-by-step explanation:

Slope-intercept form is represented by the equation y = mx + b. We can write an equation in point-slope form first, then convert it to that form.  

1) First, find the slope of the equation. Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$ and substitute the x and y values of the given points into it. Then, simplify:

$m = \frac{(-6)-(3)}{(3)-(0)}\\m = \frac{-6-3}{3-0}\\m = \frac{-9}{3}\\m = -3$

Thus, the slope is -3.

2) Now, use the point-slope formula, $y-y_1 = m (x-x_1)$ and substitute values for $m$, $x_1$, and $y_1$. From there, we can isolate y to convert the equation into slope-intercept form.

Since $m$ represents the slope, substitute -3 in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine) and substitute its x and y values into the formula, too. (I chose (0,3), as shown below). Finally, isolate y to find the answer:

$y-3 = -3(x-0)\\y-3 = -3x\\y = -3x + 3$