Identify an equation in slope-intercept form for the line parallel toy = 5x + 2 that passes through (–6, –1).

1 answer:

7 0

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We know that if 2 lines are parallel to one another, their slopes are exactly the same. So the slope of the new line is 5, just like the slope of the original line. We also have a coordinate in the form of (x, y) to fit into that line equation and solve it for b. Like this: -1 = 5(-6) + b and -1 = -30 + b and b = 29. Now we can rewrite the equation fitting in the given slope and the newly found y-intercept value of 29: y = 5x + 29 is the new line.

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Remark
This is costing you an awful lot of points, but it is a little hard to read. If I'm not interpreting it correctly, leave some sort of note below my answer.

Question One
In the first question you want a line that is parallel to x = 4 and goes through the point (-7,3). If I'm reading this correctly then the line you want is x = -7. You only need the x value of the given point. I'll put a graph there to show you what it looks like on a grid. The graph is the left one for this question.

Question Two
Here I think you want the line going through (5,-1) and perpendicular to y = 4x - 7. I will make a graph for that one as well.

Begin with the slope
Two lines are perpendicular to each other if their slopes multiply to - 1
Given slope (m1) = 4
perpendicular slope = m2

Formula
m1 * m2 = - 1
4 * m2 = -1 Divide by 4
m2 = -1/4

So far what you have is
y = (-1/4)x + b

Now use the given point to solve for b
x = 5
y = - 1
b = ??

-1 = (-1/4)*5 + b
-1 = -5/4 + b Add 5/4 to both sides
-1 + 5/4 + b Make -1 into -4/4
b = -4/4 + 5/4
b = (-4 + 5)/4
b = 1/4

So the line that you want is
y = (-1/4) x + 1/4

Answers
One: x = - 7
Two: y = (-1/4)x + 1/4

Note
The right graph is of y = 4x - 7 and y = (-1/4)x + 1/4