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
Aug 5, 2017

Slope intercept form: y=5x+11
Point slope form: (y+4)=5(x3)
Standard form: 5x+y=11

Explanation:

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

m=riserun=y2y1x2x1=1(4)23=51=5

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

(yy1)=m(xx1)

We'll choose the first point, P:

(y(4))=5(x3)

Which simplifies to:

(y+4)=5(x3)

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!