How do you write the equation of a line in slope intercept, point slope and standard form given P: (3, -4) and Q: (2,1)?

1 Answer
David G.
Aug 5, 2017

Slope intercept form: y=−5x+11
Point slope form: (y+4)=−5(x−3)
Standard form: −5x+y=11

Explanation:

First step is to find the slope (gradient), m:

m=riserun=y2−y1x2−x1=1−(−4)2−3=5−1=−5

To write the line in 'point slope' form we can choose either point and substitute it into this form:

(y−y1)=m(x−x1)

We'll choose the first point, P:

(y−(−4))=−5(x−3)

Which simplifies to:

(y+4)=−5(x−3)

To write it in 'slope intercept' or 'standard' form, we need to find the y-intercept.

To do so we use one of the points in the form for slope intercept:

y=mx+c

Let's substitute in point Q to keep it interesting:

1=−5(2)+c

Rearranging, c=11.

We can immediately write the equation of the line in standard form:

y=−5x+11

Standard form is:

ax+by=c

We get to it by moving the x term in slope intercept form to the left of the equals sign:

−5x+y=11

And we're done!

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