Question

Q

Answer 1

Answer:

$y = \frac{1}{2} x+7$

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: $\frac{y2-y1}{x2-x1}$

Given points: (-6, 4), (6, 10)

(-6, 4) = (x1, y1)

(6, 10) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the slope formula:

$\frac{10-4}{6-(-6)}$

Simplify:

10 - 4 = 6

6 - (-6) = 6 + 6 = 12

$\frac{6}{12}=\frac{1}{2}$

The slope is $\frac{1}{2}$.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (6, 10)) into the equation and solve for b:

$10 = \frac{1}{2}(6)+b$

10 = 3 + b

7 = b

The y-intercept is 7.

Now that we know the slope and the y-intercept, we can write the equation:

$y = \frac{1}{2} x+7$