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