Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-8,-7); y=-4x+3
To find the equation of a line parallel to the given equation, we first note that parallel lines have the same slope. Therefore, the slope of the new line will also be -4.
Using the point-slope form of a linear equation, where (x₁, y₁) is the given point and m is the slope:
y - y₁ = m(x - x₁)
We substitute the values (-8, -7) for (x₁, y₁) and -4 for m:
y - (-7) = -4(x - (-8))
Simplifying and rearranging the equation:
y + 7 = -4(x + 8)
Distributing -4:
y + 7 = -4x - 32
Finally, solving for y by subtracting 7 from both sides:
y = -4x - 32 - 7
Simplifying:
y = -4x - 39
The equation of the line passing through the point (-8, -7) and parallel to the graph of y = -4x + 3 can be written in slope-intercept form as y = -4x - 39.