Section 2.3 Equations of a Line 161 Furthermore, because the point (1,4) is on the line, it is a solution to the equation. Therefore, if we substitute (1,4) for x and y in the equation, we can solve 4 3112 b 4 3 b 1 b Thus, the slope-intercept form is . Skill Practice 6. Use slope-intercept form to find an equation of the line with slope 2 and passing through (3,5). y 3x 1 Calculator Connections Topic: Using the Value Feature The Value feature of a graphing calculator prompts the user for a value of x, and then returns the corresponding y-value of an equation. We can check the answer to Example 4 by graphing the equation, y3x 1. Using the Value feature, we see that the line passes through the point (1, 4) as expected. 2. The Point-Slope Formula In Example 4, we used the slope-intercept form of a line to construct an equation of a line given its slope and a known point on the line. Here we provide another tool called the point-slope formula that (as its name suggests) can accomplish the same result. Suppose a nonvertical line passes through a given point ( ) and has slope m. If (x, y) is any other point on the line, then Slope formula x1, y1 Clear fractions. m m1x x12 y y1 x x1 y y1 x x1 m1x x12 y y1 or 1x x12 y y1 m1x x1 Point-slope formula 2 for b. Answer 6. y 2x 1
miller_intermediate_algebra_4e_ch1_3
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