Expert: Josh - 10/12/2007

Question
For each line, use the given conditions to write an equation in the point-slope form and the slope-intercept form.

Slope = 4, passing through (1, 3)
Slope = 8, passing through (4, –1)
Slope = –5, passing through (–4, –2)
Slope = –2, passing through (0, –3)


Answer
Hi Sean,

For a straight line, the equation may be obtained in one of two ways:

Slope-intercept form:
Given the gradient (or slope) of a line "m" and the point where the line crosses the vertical axis (at y=b), the equation is given by y=mx+b

Point-slope form:
Given a point (xo,yo) that lies on the line, knowing the slope "m", you may write the equation as (y-yo)=m(x-xo).

Given the information you have got, it's easier to do it the second way. For the first question, m=4, xo=1, yo=3. Writing in point-slope form, (y-3)=4(x-1)......[*]

To convert this into the slope-intercept form, we can (i) expand the equation and rearrange it into something consistent with y=mx+b, OR (ii) find b (the y-intercept) by evaluating the equation in [*] putting x=0.

Method (i): y-3=4(x-1) is equivalent to y-3=4x-4. Adding 3 to both sides yields y=4x-1; exactly what we need.

Method (ii): From (y-3)=4(x-1), put x=0. (Reason: by definition, the y-intercept, the point "b" where the line crosses the vertical axis occurs at x=0. That's why we let x=0 in order to find the y-intercept). Now, with x=0, let y=b. We have b-3=4(0-1), i.e., b=-4+3, b=-1.
So, the slope-intercept form is y=4x-1, since the slope m=4.

Good luck