Writing Linear Equations Given Two Points

You must remember…. When we are given two points, we can use the slope formula to find the slope of the line between them. Example: You are given the points (4, 7) and (2, 6). Find the slope. m = rise = y2 – y1 = 6 – 7 = 1 run x2 – x1 2 – 4 2

Writing an Equation of a Line Given Two Points Step 1: Find the slope. Substitute the coordinates of the two given points into the formula for slope, m = y2 – y1 x2 – x1 Step 2: Find the y-intercept. Substitute the slope m and the coordinates of one of the points into the slope-intercept form, y = mx +b, and solve for the y-intercept. Step 3: Write an equation of the line. Substitute the slope m and the y-intercept b into the slope-intercept form, y = mx + b.

Writing an Equation Given Two Points Write an of a line that passes through the points (3, 5) and (4, 7). First we must find the slope of the line. We need to use the slope formula to do this. m = y2 – y1 = 7 – 5 = 2 = 2 x2 – x1 4 – 3 1 Now we must find the y-intercept. y = mx + b 5 = 2(3) + b 5 = 6 + b Subtract 6 from both sides. -1 = b Now let’s write the equation of the line. y = 2x – 1

Examples Write an equation of a line that passes through the points (9, 4) and (8, 7). First we must find the slope of the line. We need to use the slope formula to do this. m = y2 – y1 = 7 – 4 = 3 = -3 x2 – x1 8 – 9 -1 Now we must find the y-intercept. y = mx + b 4 = -3(9) + b 4 = -27 + b Add 27 to both sides. 31 = b Now let’s write the equation of the line. y = -3x + 31

Examples Write an equation of a line that passes through the points (6, 1) and (2, 4). First we must find the slope of the line. We need to use the slope formula to do this. m = y2 – y1 = 4 – 1 = 3 x2 – x1 2 – 6 -4 Now we must find the y-intercept. y = mx + b 1 = (-3/4)(6) + b 1 = -4.5 + b Add 4.5 to both sides. 5.5 = b Now let’s write the equation of the line. y = (-3/4)x + 5.5