WRITE THE EQUATION OF A LINE
Formulas
Slope formula:
Slope-intercept form:
Point-slope form
1. Given: Slope (m) and the y-intercept (0, b)
Use: Slope-intercept form:
Example: Write the equation of a line with a slope of 5 and a y-intercept of (0, -7).
Since m = 5 and (0, -7) is the y-intercept, b = -7, then substituting into the form will give us
the equation of the line: 5 7
2. Given: Slope (m) and point (x
1
, y
1
)
Use: Point-slope form:
Example: Write the equation of a line in slope-intercept form, with a slope of -3 and goes through the point (3, -2).
Since m=-3 and (3, -2) is the point (x
1
, y
1
), substitute into the form
.
2
3
3
2 3 9
3 7
3. Given: Two points (x
1
, y
1
) and (x
2
, y
2
)
Use: a.
b. Pick one of the two points and use point-slope form
Example: Write the equation of a line in slope-intercept form that goes through the two points (-1, 4) and (2, -2).
a.
2 b. m = -2, using point (-1, 4)
4 2
1
4 2
1
4 2 2
2 2
4. Given: An equation of a line with a parallel or perpendicular relationship and a point (x
1,
y
1
).
Use: The given equation of a line and the relationship to find the slope. (Parallel use the same slope,
perpendicular use the opposite-reciprocal slope). Then use point-slope form.
Example: Write the equation of a line in slope-intercept form that is perpendicular to 2x-3y = 6 and goes through
the point (-1, 2).
a. Solve the given equation for y to identify the slope.
2 3 6
3 2 6
2
3
2,
2
3
b. Use
because it is the perpendicular slope to 2x-3y = 6, and point (-1, 2).
2
3
2
x 1
2
3
2
3
2
3
2
1
2
