Line j passes through point (2,0) and is perpendicular to the graph of y=1/4x-3. Line k is parallel to line j and passes through point (-1,6). What is the equation in slope-intercept form of line k?

Question

Please explain the steps as I've never done this before so I can learn how to get the answer myself.

Answer 1

This needs to be split up into sections. Make sure you work out each small step and don't skip them!

We want to find the EQUATION of a line in SLOPE - INTERCEPT form. This means in the form of:

y = mx + b (m = the slope and b = the y intercept)

Sections:

1. Line j
2. Line k

Section 1:

Line j is "perpendicular to the graph of y=1/4x-3". This means that the "slope" of j is at right angles to that of the graph.

Slope of graph given = 1/4

A simple to find a slope perpendicular to this is to take -1 and DIVIDE IT by the SLOPE of the graph: -1/(1/4) = -4

Slope of line j = -4, so we have m = -4

now, we can use the equation y-y₁=m(x-x₁) to find the slope intercept formula. We know that the line j goes through point (2,0), so we substitute this in:

y - 0 = -4(x - 2)

FINAL ANSWER: y = -4x +8

Section 2

Line k is parallel to line j, so has slope = -4. it runs through point (-1,6), substituting in gives:

y - 6 = -4(x - (-1))

y - 6 = -4x - 4

y = -4x - 4 + 6

y = -4x + 2