What is the slope-intercept form of the line passing through (5,1) and (0,−6)?

3 Answers
IHate P. · Stefan V.
Mar 3, 2018

The general slope intercept form of a line is

y=mx+c

where m is the slope of the line and c is its y-intercept (the point at which the line cuts the y axis).

Explanation:

First, get all the terms of the equation. Let us calculate the slope.

slope=y2−y1x2−x1

=−6−10−5

=75

The y-intercept of the line is already given. It is −6 since the x coordinate of the line is zero when it intersects the y axis.

c=−6

Use the equation.

y=(75)x−6

Shiva Prakash M V
Mar 3, 2018

y=1.4x+6

Explanation:

P≡(5,1)
Q≡(0,−6)
m=−6−10−5=−7−5
m=1.4
c=1−1.4×5=1−7
c=6
y=mx+c
y=1.4x+6

mrcoffie
Mar 3, 2018

One answer is: (y−1)=75(x−5)
the other is: (y+6)=75(x−0)

Explanation:

The slope-intercept form of a line tells you what you need to find first: the slope.
Find slope using m=y2−y1x2−x1
where (x1,y1) and (x2,y2) are the given two points
(5,1) and (0,−6):

m=−6−10−5=−7−5=75

You can see this is in both answers.

Now choose either point and plug in to the slope-intercept form of a line: (y−y1)=m(x−x1)

Choosing the first point results in the first answer and choosing the second point yields the second answer. Also note that the second point is technically the y-intercept, so you could write the equation in slope-intercept form (y=mx+b): y=75x−6.

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