Slope-Intercept Form Of A Linear Equation Examples Worksheet - Johnny Wolfe, Jay High School, 2001
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11Slope-Intercept Form of a Linear Equation Examples
1. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice
that b is the y-intercept of AB . Suppose you want to find an equation for AB . Let
m represent the slope of the line.
−
y
b
Use the definition of
m =
−
x
0
slope. AB passes through
y −
b
(x, y) and (0, b), so that
m =
x
= x, x
= 0, y
= y, and
x
2
1
2
y
= b. Solve for y.
mx = y – b
1
y = mx + b
2.
Slope-Intercept Form of a Linear
The slope-intercept form of the equation
Equation
of a line is y = mx + b, where m is the
slope and b is the y-intercept
Let (x, y) and (x
, y
) be points on
1
1
Derivation of point-slope
−
y
y
form
1
line AB. Then the slope, m is
.
−
x
x
1
Therefore, m(x – x
) = y – y
.
1
1
3. Suppose you are given the slope and y-intercept of a line. You can find an
equation of the line by substituting these values into the slope-intercept form of
2
− and its y-intercept is 14, an
the equation. For example, if the slope of a line is
3
2
−
equation of the line is y =
x + 14. The standard form of this equation is
3
2x + 3y = 42.
Recall that the standard form of the equation of a line is Ax + By = C. If B ≠ 0,
the slope and y-intercept can be found by changing the equation to slope-
intercept form.
Slope-Intercept Form of a Linear Equation Johnny Wolfe
Jay High School Santa Rosa County
Florida
September 30, 2001
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