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.
(-2,-3);y=-4x+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 the given equation, we notice that parallel lines have the same slope. Since the given equation is in slope-intercept form y = mx + b, where m is the slope, we can determine the slope of the given equation as -4.
Now we can use the point-slope form of a linear equation (y - y1) = m(x - x1) and substitute the given point (-2, -3) and slope -4 into the equation:
(y - (-3)) = -4(x - (-2))
Simplifying the equation gives:
y + 3 = -4(x + 2)
Expanding the equation further:
y + 3 = -4x - 8
To get the equation in slope-intercept form, we isolate y on one side of the equation:
y = -4x - 8 - 3
This simplifies to:
y = -4x - 11
Therefore, the equation of the line that passes through the given point (-2,-3) and is parallel to the graph of y = -4x + 5 is y = -4x - 11.