Slope-Intercept Form
In the equation y = 2x + 3, we know that 2 is the slope of the line and the coefficient of x,
so what does the 3 represent?
Let x = 0
y = 2(0) + 3
y=0+3
y=3
Therefore, the constant at the end of the equation
represents the y-intercept
Since both the slope and the y-intercept can be read directly from the equation of a line,
we say such equations are in slope-intercept form.
y  mx  b
SLOPE-INTERCEPT FORM:
The slope-intercept form of the equation of a line with slope m and y-intercept
(0,b).
Ex: Write the equation of a line given m =
2
and y-intercept (0,-1).
3
1
Ex: m = ; y-intercept (0,-4)
2
Ex: m = -1; y-intercept (0,8)
Ex: m =3; y-intercept (0.0)
Ex: m =0; y-intercept (0,2)
Graphing a Line from Slope-intercept Form
Process:
1) Solve for y so equation is in y = mx + b form
2) Graph the y-intercept.
3) Using the slope, find other points along the line, beginning at the y-intercept.
4) Join the points of the line (Connect the dots…la la lala)
Ex: 2x – 3y = 3
Examples:
1) y = 3x + 2
5) x + 2y = 4
2) y = 4x – 4
6) x + 3y = 12
3) 2x + y = -5
4) 3x + y = -2
Graphing a Line Given a Point and the Slope
Process:
1) Plot the given coordinates
2) Use the slope to plot other points on the line, beginning at the coordinates.
Ex: Graph the line through (-2,3) with m = -4.
Examples:
1) (-2,3); m =
1
2
5) (3,2); m = 0
2) (-4,-1); m =
3
4
3) (1,-5); m =
6) (3,-2); undefined slope
2
5
4) (2,-1); m =
1
3
7) (2,4); undefined slope
Write an Equation of a Line Given Slope and a Point on the
Line
y  y1
 m . If we multiply both sides by x  x1 (eliminating the denominator),
x  x1
we get: y  y1  m( x  x1 )
We know
Point-Slope Form of a Line: y  y1  m( x  x1 )
Ex: Find the equation of the line passing through (-2,4) with m = -3
Examples:
1) Through (4,2), m =
3
5
2) Through (-1,3), m = -2
3) Through (5,2), m =
1
3
4) Through (4,1), m = 2
5) Through (2,7), m = 3
6) Through (3,-10), m = -2
Write an Equation Given 2 Points
Given the points (-2,5) and (3,4), find the equation of the line.
Process:
1) Using the two points, find the slope of the line.
2) Using the found slope and either of the 2 points, find the equation of the line with the
point-slope formula.
Examples:
1) (8,5) and (9,6)
2) (4,10) and (6,12)
4) (-2,-1) and (3,-4) 5) (0,-2) and (-3,0)
1 3
1 5
7) ( , ) and ( , )
2 2
4 4
3) (-1,-7) and (-8,-2)
6) (-4,0) and (0,2)
Enrichment:
1) Write the equation of a line through (2,-3) and parallel to 3x = 4y + 5
2) Through (-1,4) and perpendicular to 2x + 3y = 8
3) Perpendicular to x – 2y = 7 with a y-intercept = (0,-3)
4) Parallel to 5x = 2y + 10 with a y-intercept = (0,4)