Question

Write an equation of the line passing through the point (4, 3) that is perpendicular to the line 4x - 7y=9.

An equation of the line is y=_x+_

Answer 1

y = (7/4)x - 4

Explanation:

Rewrite the equation in standard format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

4x - 7y=9

- 7y=9-4x

y=(-4x + 9)/(-7)

y = -(4/7)x - (9/7)

This line has a slope of -(4/7). A line perpendicular to this line will have a slope that is the negative inverse of the reference line. The prependicular line will have a slope of (7/4) [the negative inverse of -(4/7)].

We can now write the new line as

y = (7/4)x + b

We need a value of b that forces the line to go through point (4,3). This can be di=one by entering (4,3) into the perpendicular equation (y = (7/4)x + b) and solve for b:

y = (7/4)x + b

3 = (7/4)*4 + b for point (4,3)

3 = 7 + b

b = -4

The equation is y = (7/4)x - 4

See the attached graph.