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Writing Equations Using Slope-Intercept Form Objective: As an alternate to point-slope form, the learner will use slope-intercept form to write the equation of a line. Prerequisite skills: The learner should be familiar with graphing using slope-intercept form Lesson Plan: The slope-intercept form of an equation is not only useful in graphing lines, it helps us to write an equation of a line given some key information. Recall that for y = mx + b, m is the slope and b is the y-intercept. If we know m and b, we can write the equation of a line by inserting these numbers into y=mx + b For example: 1. Given m = 3 and b = 5, the equation is y = 3x + 5 2. Given m = -2 and b = ½, the equation is y = -2x + ½ Now you try. Write the equation of a line in slope-intercept form given the following. Simplify if possible. 1. m = 7 and b = 4 2. m = -6 and b = ½ 3. m = 0 and b = 8 4. m = -2 and b = 0 1 Writing Equations Using Slope-Intercept Form What if we are given m and a point (x,y) but not b? Can we still write the equation of the line? We can use Slope-intercept form, y = mx + b, to write the equation of a line because we’ve been given m, x and y. Just plug in and solve for b! The steps to writing an equation using slope-intercept form are as follows. 1. Identify x, y and m from information given 2. Substitute in x, y and m into y = mx + b 3. Solve for b 4. Write the equation y = mx + b substituting in JUST m and b Example: Write the equation in slope-intercept form given the slope and a point. (2,1), m = 3 x = 2, y = 1, m = 3 1 = 3(2) + b 1=6+b -5 = b identify x, y and m substitute x, y and m into y = mx + b simplify 3 times 2 solve for b by subtracting 6 from both sides Now write the equation of the line by substituting in m and b into y = mx + b y = 3x - 5 Let’s work these together. Write the equation in slope-intercept form given the slope and a point. (1,3), m = -2 (4,-2), m = -¼ 2 Writing Equations Using Slope-Intercept Form Sometimes you are given two points on the line but no slope. We’ll still use the slope-intercept form, but first we have to find the slope ourselves. Follow these steps: 1. Find the slope using the 2 given points and the formula for slope 2. Use one of the points and the slope to substitute into slope-intercept form 3. Solve for b 4. Write the equation y = mx + b substituting in JUST m and b Here’s an example: Given points (0,2) and (4,3) write the equation of a line in slope-intercept form. Recall that slope, m = m= = You can use either point to substitute into y = mx + b. I will use (0,2). x = 0, y = 2, m = identify x, y and m 2 = (0) + b substitute into y = mx + b 2=0+b 2=b simplify solve for b Use this b and m to write your equation: y= x+2 Let’s work these together. Given points (0,0) and (-1,-5) write the equation of a line in slope-intercept form. Given points (2,2) and (4,-1) write the equation of a line in slope-intercept form. 3