Final answer:
The equation of the line that is parallel to 4x+3y=-45 and passes through the point (-9, -5) is y = (-4/3)x - 17. This equation is derived by finding the slope of the original line and using the point-slope form with the given point.
Step-by-step explanation:
The student asked for the equation of a line in slope-intercept form that is parallel to the given line 4x+3y=-45 and passes through the point (-9,-5). To find this, we first need to write the given line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, solve for y in terms of x:
3y = -4x - 45
y = (-4/3)x - 15
The slope (m) of the given line is -4/3. A line that is parallel to another has the same slope. Therefore, the slope of the parallel line is also -4/3.
We can use the slope and the given point (-9, -5) to find the y-intercept (b) of the new line. The equation for this is:
y - y1 = m(x - x1)
Plugging in the values gives us:
-5 - (-9)(-4/3) = -5 - 12 = -17
So, the equation of the line in slope-intercept form that is parallel to the given line and goes through the point (-9, -5) is:
y = (-4/3)x - 17