- Slides: 6
Writing Linear Equations Given Two Points On the Line Using the "Slope – Intercept" Form
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Getting Started Any two points will determine a line The line connecting these two points has an equation that describes this line. Our job is to find this equation when we are only given two points. We will be using the slope – intercept form of a linear equation y = mx + b, and the point – slope form of a linear equation. y – y 1 = m(x – x 1)
Using the Slope – Intercept Form First, let's review the slope – intercept form of a linear equation. y = mx + b, (x , y) are ordered pairs that lie on the line m is the slope of the line b is the y – intercept (or where the line crosses the y – axis)
Using the Slope – Intercept Form There are 3 steps involved in writing the equation of a line in slope – intercept form when we are given two points. STEP 1: Use the two points to find the slope of the line (x 1 , y 1) and (x 2 , y 2) STEP 2: Use the slope and ONE of the points to find the y – intercept Use y = mx + b. Substitute the value of m from step 1 and substitute either one of the points (x , y). Then solve the equation for b STEP 3: Use the slope and y – intercept to write the equation of the line Write y = mx + b, but replace the m and b with the values obtained from steps 1 and 2.
Using the Slope – Intercept Form PROBLEM: Write the equation of a line in slope – intercept form that passes through the points (2 , – 3) and (– 3 , 7) STEP 1: Use the two points to find the slope of the line So, m = – 2 STEP 2: Use the slope and ONE of the points to find the y – intercept So, b = 1 STEP 3: Use the slope and y – intercept to write the equation of the line y = mx + b SOLUTION: y = – 2 x + 1 NEATLY Pick either of the points. Suppose we pick the point (2 , – 3). Substitute the x and y values along with the m value from step 1 into the equation y = mx + b. SHOW YOUR – 3 = (– 2)(2) + b Solve this equation for b. – 3 = – 4 + b WORK 1=b