162 Chapter 2 Linear Equations in Two Variables and Functions The Point-Slope Formula The point-slope formula is given by y y1 m1x x12 1x1, y12 where m is the slope of the line and is a known point on the line. The point-slope formula is used specifically to find an equation of a line when a point on the line is known and the slope is known. To illustrate the point-slope formula, we will repeat the problem from Example 4. Using the Point-Slope Formula to Find an Equation of a Line Example 5 Use the point-slope formula to find an equation of the line having a slope of 3 and passing through the point (1, 4). Write the answer in slope-intercept form. Solution: and 1x1, y12 11,42 Apply the point-slope formula. Simplify. y y1 m1x x12 y 142 31x 12 y 4 31x 12 To write the answer in slope-intercept form, clear parentheses and solve for y. Clear parentheses. Solve for y.The answer is written in slopeintercept form. Notice that this is the same equation as in Example 4. y 4 3x 3 y 3x 1 Skill Practice 7. Use the point-slope formula to write an equation for the line passing through the point ( 2, 6 ) and having a slope of 5. Write the answer in slope-intercept form. m 3 Answer 7. y 5x 16 TIP: The solution to Example 5 can also be written in standard form, Ax By C. Slope-intercept form Add 3x to both sides. Standard form y 3x 1 3x y 3x 3x 1 3x y 1 In general, we will write the solution in slope-intercept form, because the slope and y-intercept can be easily identified.
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