Write the equation and y-intercept of the line graphed below. Write the standard form equation of the line that passes through the points (-6, -4) and (2, 0)

To find the equation of the line and the y-intercept, we start with the two points given: (-6, -4) and (2, 0).

1. Find the slope (m):

[

m = frac{y_2 – y_1}{x_2 – x_1} = frac{0 – (-4)}{2 – (-6)} = frac{4}{8} = frac{1}{2}

]

2. Use the point-slope form to find the equation:

The point-slope formula is:

[

y – y_1 = m(x – x_1)

]

Using point (2, 0):

[

y – 0 = frac{1}{2}(x – 2)

]

Simplifying this:

[

y = frac{1}{2}x – 1

]

3. Get the y-intercept:

The y-intercept occurs where (x = 0):

[

y = frac{1}{2}(0) – 1 = -1

]

4. Standard form:

To convert (y = frac{1}{2}x – 1) into standard form (Ax + By = C):

Multiply everything by 2 to eliminate the