Question

Write an equation in slope-intercept for the line that goes

Answer 1

Answer:

y = 1/3x - 4

Step-by-step explanation:

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Answer 2

Answer:

$y = \frac{1}{3} x-4$  

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of the given points into the formula and solve:

$m=\frac{(-2)-(-3)}{(6)-(3)} \\m = \frac{-2+3}{6-3} \\m = \frac{1}{3}$

Thus, the slope is $\frac{1}{3}$.

2) Next, write the equation of the line using the point-slope formula $y-y_1 = m (x-x_1)$. (From there, we can convert it to slope-intercept form.) Substitute $m$, $x_1$, and $y_1$ for real values.

Since $m$ represents the slope, substitute $\frac{1}{3}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, substitute the x and y values of either one of the given points (it doesn't matter which one, it will equal the same thing) into the formula as well. I chose (3, -3), as shown below. From there, convert the point-slope form of the equation to slope-intercept form by isolating y:

$y-(-3) = \frac{1}{3} (x-3)\\y + 3=\frac{1}{3} x-1\\y = \frac{1}{3} x-4$