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, - 6); y = - 5x + 5
Write an equation for the line in slope-intercept form. __
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
To find the equation of a line parallel to a given line, we can use the fact that parallel lines have the same slope.
The given equation is in slope-intercept form y = mx + b, where m is the slope. So, the given line has a slope of -5.
To find the equation of the line parallel to this, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using the point (-8, -6) and the slope -5, we can write the equation as:
y - (-6) = -5(x - (-8))
Simplifying,
y + 6 = -5(x + 8)
Expanding,
y + 6 = -5x - 40
Rearranging to slope-intercept form,
y = -5x - 40 - 6
y = -5x - 46
Therefore, the equation for the line in slope-intercept form is y = -5x - 46.