Free Algebra
Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

Math solver on your site

Please use this form if you would like
to have this math solver on your website,
free of charge.

Name:

Email:

Your Website:

Msg:

Slope-Intercept Form for the Equation of a Line

We have found the equation of a line in point-slope form and in standard form.

Another form for the equation of a line is the slope-intercept form. We can derive this from the point-slope form.

We begin with the point-slope form for the equation of a line. Use the y-intercept, (0, b), for the point (x₁, y₁).That is, substitute 0 for x₁ and b for y₁.	y - y₁ y - b	= m(x - x₁) = m(x - 0)
Simplify the right side. Add b to both sides.	y - b y	= mx = mx + b

Definition â€” Slope-Intercept Form for the Equation of a Line

The slope-intercept form for the equation of a line with slope m and y-intercept (0, b) is:

y = mx + b

Example 1

Find the equation of the line with y-intercept (0, -6) and slope 2.

Write the equation in slope-intercept form.

Solution

Substitute the given values in the slope-intercept form of the equation.

Both the slope, m, and the y-intercept, (0, b), are given: m is 2 and b is -6.

Simplify.

y = mx + b

y = 2x + (-6)

y = 2x - 6

The slope-intercept form of the equation of the line with y-intercept (0, -6) and slope 2 is y = 2x - 6.

Note â€” To Write the Equation of a Line Given Two Points

Here are two ways to write the equation of a line when given two points:

Use the Point-Slope Form

Step 1 Find the slope.

Step 2 Substitute the slope, m, and the coordinates of one of the points, (x₁, y₁), in y - y₁ = m(x - x₁)

Step 3 Simplify.

Use the Slope-Intercept Form

Step 1 Find the slope.

Step 2 Substitute the slope, m, and the coordinates of one of the points, (x, y), in y = mx + b

Then, solve the equation for b.

Step 3 Substitute the value of m and the value b in y = mx + b.