Find the equation of a line with the properties given. Write the equation in the form indicated.
-Through (2, 4) and parallel to the line whose equation is 5x + y = 9; slope-intercept form
B) y = 5x - 14
C) y = -5x + 14
D) y = -5x - 14

Question

Find the equation of a line with the properties given. Write the equation in the form indicated.
-Through (2, 4) and parallel to the line whose equation is 5x + y = 9; slope-intercept form
B) y = 5x - 14 
C) y = -5x + 14 
D) y = -5x - 14

Quizplus · Accepted Answer

To find the equation of a line parallel to another line, we know that they will have the same slope.

So, first we need to find the slope of the line whose equation is 5x + y = 9. We can rewrite this equation in slope-intercept form (y = mx + b) by subtracting 5x from both sides and then solving for y:

y = -5x + 9

So the slope of this line is -5.

Now we can use the point-slope form of the equation of a line to find the equation of the line we want:

y - y1 = m(x - x1)

where (x1, y1) is the point we're given (in this case, (2, 4)) and m is the slope we just found (-5).

Plugging in these values gives us:

y - 4 = -5(x - 2)

Expanding the right side and solving for y gives us:

y = -5x + 14

which matches choice (C). To find the equation of a line that is parallel to the given line, we need to use the fact that parallel lines have the same slope. The slope of the given line can be found by rearranging the equation into slope-intercept form: y = -5x + 9. So the slope of any line parallel to this one will also be -5.

To find the equation of the line passing through (2,4) with slope -5, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1,y1) is the given point and m is the slope. Plugging in the values we get:

y - 4 = -5(x - 2)

Simplifying gives:

y = -5x + 14

which is in slope-intercept form. Therefore, the answer is C.

Find the Equation of a Line with the Properties Given