Jack B. answered • 09/29/21
Experienced Ivy League Test-Prep Tutor and College Admissions Advisor
1) A straight line takes the form: y = mx + b, where m refers to the slope of the line.
2) Now, you need to keep in mind that two lines are parallel when they have the same slope.
3) The slope of a line is the rise of the line over the run of the line, which is another way of saying the change in the y-coordinate divided by the change in the x-coordinate.
Use the second half of the information first: The line is parallel to another line that passes through the following points:
(-2, 3.5) and (4, 5)
To find the slope, you must subtract the x and y coordinates of one of these points from the x and y coordinates of the other point. The order doesn't matter - which point you subtract from -, but you do need to be consistent. Subtract one of the y-coordinates from the other y-coordinate. Then subtract one of the x-coordinates from the other one.
Let's start with the second point (4, 5) and subtract from this point the coordinates of the point at (-2, 3.5):
y-coordinate subtraction: 5 minus 3.5 = 1.5
x-coordinate subtraction: 4 minus -2 = 4 + 2 = 6
Divide the y-subtraction answer by the x-subtraction answer: 1.5/6
You can simplify this number - (1.5/6) - to 1/4
This is the slope of the line that passes through the points (-2, 3.5) and (4, 5).
Go back to your first equation:
y = mx + b
You now have your slope, which is the m value.
y = (1/4)x + b
Since your assignment is to find the equation of the line that passes through the point (4, -6), you can now plug in those values to the preceding equation:
-6 = (1/4) 4 + b
Solve this equation to get your b value, which is the y-intercept:
-6 = 1 + b
-7 = b
And so (ta-da!) you have now found the b value! You know the slope, which is the m value . . . and you know the b value . . . and so the answer is:
y = (1/4) x -7
or if you prefer:
y = x/4 - 7
