Question

Write an equation in slope-intercept form from the points (0, 3) and (-4,-1)

Answer 1

Answer:

y = x + 3

Step-by-step explanation:

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

1) First, find the slope of the line. 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 to find the slope, or $m$:

$m = \frac{(-1)-(3)}{(-4)-(0)} \\m = \frac{-1-3}{-4-0} \\m = \frac{-4}{-4} \\m = 1$

Thus, the slope of the line must be 1.

2) Now, since we know a point the line intersects and its slope, 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 convert the equation into slope-intercept form.

Since $m$ represents the slope, substitute 1 in its place. Since $x_1$ and $y_1$ represent the x and y values of a point the line intersects, choose any one of the given points (either one is fine) and substitute its x and y values into the equation, too. (I chose (0,3).) Finally, isolate y to find the answer:

$y-3=1(x-0)\\y-3 = x\\y = x + 3$