Slope-Intercept FormSlope-Intercept Form

Slope-Intercept FormSlope-Intercept Form

y=mx + by=mx + bm is the SLOPEm is the SLOPEb is the Y-INTERCEPT (where the line b is the Y-INTERCEPT (where the line

crosses the y-axis)crosses the y-axis)the “x” and “y” must be present at the the “x” and “y” must be present at the

end within the equation to graph the lineend within the equation to graph the line

Slope-Intercept Form of the Slope-Intercept Form of the Equation of a LineEquation of a Line

The line with slope The line with slope ““mm”” and y-intercept has the equation and y-intercept has the equation y = m x + b.y = m x + b.

y=3x-6 y=3x-6

The slope is 3The slope is 3

The y intercept is The y intercept is -6-6

Writing an EquationWriting an Equation

Write the equation of the line with slope 3/8 Write the equation of the line with slope 3/8 and y-intercept 5.and y-intercept 5.

Use slope intercept form:Use slope intercept form:

y = mx + by = mx + b

Substitute in for m and bSubstitute in for m and b

Writing an EquationWriting an Equation

y = 3/8 x + 5 y = 3/8 x + 5

What if IWhat if I’’m Given the Slope and m Given the Slope and an Ordered Pair to form a an Ordered Pair to form a

slope-int equationslope-int equationm = 3, (5,-2)m = 3, (5,-2)y = mx + by = mx + by = 3x + by = 3x + by = 3(5) + by = 3(5) + b -2 = 3(5) + b-2 = 3(5) + bSolveSolve

-2 = 3(5) + b

-2 = 15 + b

-15 -15

-17 = b

Therefore the equation is:

y = 3x -17

What If IWhat If I’’m Given m Given Two Ordered Pairs?Two Ordered Pairs?

Write an equation in slope-intercept form Write an equation in slope-intercept form of a line passing through each pair of of a line passing through each pair of points.points.

Step One – Find the slopeStep One – Find the slopeStep Two – Input one set of ordered pairs Step Two – Input one set of ordered pairs

into the slope intercept form and solve for into the slope intercept form and solve for b (y – int)b (y – int)

You TryYou Try

Write the equation of a line with slope -.5 Write the equation of a line with slope -.5 and y-intercept -3and y-intercept -3

y = y =

Write the equation of a line with slope 4 and Write the equation of a line with slope 4 and y-intercept -5/2.y-intercept -5/2.

y =y =

You TryYou Try

Identify the slope and y intercept.Identify the slope and y intercept.y = -5x + 13y = -5x + 13

Slope: Slope: Y-Intercept:Y-Intercept:Identify the slope and y intercept.Identify the slope and y intercept.

y = 1/4x – 2y = 1/4x – 2Slope:Slope:Y-Intercept:Y-Intercept:

You TryYou Try

Write the equation of a line with slope -3 that Write the equation of a line with slope -3 that passes through pt. (2, 5)passes through pt. (2, 5)

Example: Write these Two Ordered Example: Write these Two Ordered Pairs in Slope Intercept FormPairs in Slope Intercept Form

(-4, 4) and (2, 1)(-4, 4) and (2, 1) 4 -1 = 3 or 14 -1 = 3 or 1

-4 -2 = -6 or -2-4 -2 = -6 or -2

Input slope into the formula with one set of ordered pairsInput slope into the formula with one set of ordered pairs

y2 – y1

x2 – x1

Formula for Slope

Slope Intercept Form: y = mx + b

1 = -1/2 (2) + b 1 = - 1 + b

+1 +1

2 = b

Therefore: y = -1/2x + 2

Solve