5 Ways to Convert to Slope Intercept Form

Understanding Slope Intercept Form

The slope-intercept form is a way of expressing a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful for graphing lines and finding the equation of a line given its slope and y-intercept.

Why Convert to Slope Intercept Form?

Converting to slope-intercept form can make it easier to:

• Graph lines
• Find the equation of a line given its slope and y-intercept
• Solve systems of equations
• Find the x-intercept of a line

Method 1: Converting from Standard Form

To convert from standard form (Ax + By = C) to slope-intercept form, follow these steps:

• Subtract By from both sides of the equation to get the x term by itself
• Divide both sides of the equation by A to get the x term by itself
• Rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept

Example:

Convert the equation 2x + 3y = 6 to slope-intercept form

• Subtract 2x from both sides: 3y = -2x + 6
• Divide both sides by 3: y = (-²⁄₃)x + 2

📝 Note: Make sure to divide both sides of the equation by the coefficient of y, not the coefficient of x.

Method 2: Converting from Point-Slope Form

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form, follow these steps:

• Distribute the slope to the terms inside the parentheses: y - y1 = mx - mx1
• Add y1 to both sides of the equation to get the y term by itself
• Rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept

Example:

Convert the equation y - 2 = 3(x - 1) to slope-intercept form

• Distribute the slope: y - 2 = 3x - 3
• Add 2 to both sides: y = 3x - 1

Method 3: Converting from Slope and a Point

To convert from slope and a point (m, (x1, y1)) to slope-intercept form, follow these steps:

• Write the equation in point-slope form: y - y1 = m(x - x1)
• Distribute the slope to the terms inside the parentheses: y - y1 = mx - mx1
• Add y1 to both sides of the equation to get the y term by itself
• Rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept

Example:

Convert the slope and point (2, (3, 4)) to slope-intercept form

• Write the equation in point-slope form: y - 4 = 2(x - 3)
• Distribute the slope: y - 4 = 2x - 6
• Add 4 to both sides: y = 2x - 2

Method 4: Converting from Two Points

To convert from two points ((x1, y1), (x2, y2)) to slope-intercept form, follow these steps:

• Find the slope using the formula m = (y2 - y1)/(x2 - x1)
• Write the equation in point-slope form: y - y1 = m(x - x1)
• Distribute the slope to the terms inside the parentheses: y - y1 = mx - mx1
• Add y1 to both sides of the equation to get the y term by itself
• Rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept

Example:

Convert the points (2, 3) and (4, 5) to slope-intercept form

• Find the slope: m = (5 - 3)/(4 - 2) = 1
• Write the equation in point-slope form: y - 3 = 1(x - 2)
• Distribute the slope: y - 3 = x - 2
• Add 3 to both sides: y = x + 1

Method 5: Converting from a Graph

To convert from a graph to slope-intercept form, follow these steps:

• Identify the y-intercept (the point where the line crosses the y-axis)
• Identify the slope (the ratio of the rise to the run)
• Write the equation in the form y = mx + b, where m is the slope and b is the y-intercept

Example:

Convert the graph to slope-intercept form

• Identify the y-intercept: (0, 2)
• Identify the slope: m = ³⁄₂
• Write the equation: y = (³⁄₂)x + 2

In conclusion, converting to slope-intercept form can be done using various methods, including converting from standard form, point-slope form, slope and a point, two points, and a graph. Each method requires a different set of steps, but they all involve rewriting the equation in the form y = mx + b.

Related Terms:

• Graphing slope-intercept form worksheet