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.

Question

(-9,-6); y=-5x+3

Answer 1

To find the equation of the line that passes through the point (-9, -6) and is parallel to the graph of the equation y = -5x + 3, we need to consider two main characteristics of parallel lines:

1. Parallel lines have the same slope.
2. Parallel lines have different y-intercepts.

Since the given equation y = -5x + 3 represents a line with a slope of -5, any line parallel to it will also have a slope of -5.

To write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we'll use the point (-9, -6) along with the slope -5 to find b, the y-intercept of our new line.

Using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope, we can substitute the slope and the point (-9, -6):

y - (-6) = -5(x - (-9))

Now, simplify and write it in slope-intercept form:

y + 6 = -5(x + 9)
y + 6 = -5x - 45

To get the slope-intercept form, solve for y:

y = -5x - 45 - 6
y = -5x - 51

So, the equation in slope-intercept form of the line passing through the point (-9, -6) and parallel to the given line is:

y = -5x - 51