Question

Write the slope intercept form of the equation of the line.Help

Answer 1

Answer:

Our final equation is $\bold{y = \frac{1}{4}x + 3}.$

Step-by-step explanation:

We are given a coordinate point and the slope of a line. We need to know that:

• The slope-intercept form of a line is $\text{y = mx + b},$ where m is the slope of the line and b is the y-intercept of the line.
• The point-slope formula is y - y₁ = m(x - x₁).

We want to end up at the slope-intercept form of the equation. Therefore, we can use the point-slope formula and substitute our values and solve the equation.

$y - 2 = \frac{1}{4}(x - (-4))\\\\y - 2 = \frac{1}{4}x + 1\\\\\small\boxed{\bold{y = \frac{1}{4}x + 3}}$

Therefore, we have determined that our equation in slope-intercept form is $\bold{y = \frac{1}{4}x + 3}$.

Answer 2

$\huge\boxed{y=\frac{1}{4}x+3}$

Hey! Let's start off with the point-slope form equation:

$y-y_1=m(x-x_1)$

In this equation, $m$ represents the slope and $(x_1, y_1)$ is the known point.

Substitute in the values we know:

$y-2=\frac{1}{4}(x-(-4))$

Subtracting a negative number is the same as adding a positive number.

$y-2=\frac{1}{4}(x+4)$

Distribute the $\frac{1}{4}$:

$y-2=\frac{1}{4}x+1$

Add $2$ to both sides to get the equation in slope-intercept form, which is $y=mx+b$:

$\boxed{y=\frac{1}{4}x+3}$