254 CHAPTER 2 Graphs and Functions y - y1 = m1x - x12 Point-slope form y - 2 = - 6 5 3x - 1-324 x1 = -3, y1 = 2, m= - 6 5 51y - 22 = -61x + 32 Multiply by 5. 5y - 10 = -6x - 18 Distributive property 6x + 5y = -8 Standard form Verify that we obtain the same equation if we use 12, -42 instead of 1-3, 22 in the point-slope form. S Now Try Exercise 19. NOTE The lines in Examples 1 and 2 both have negative slopes. Keep in mind that a slope of the form - A B may be interpreted as either -A B or A -B . Slope-Intercept Form As a special case of the point-slope form of the equation of a line, suppose that a line has y-intercept 10, b2. If the line has slope m, then using the point-slope form with x1 = 0 and y1 = b gives the following. y - y1 = m1x - x12 Point-slope form y - b = m1x - 02 x1 = 0, y1 = b y - b = mx Distributive property y = mx + b Solve for y. Slope The y-intercept is 10, b2. Because this result shows the slope of the line and indicates the y-intercept, it is known as the slope-intercept form of the equation of the line. Slope-Intercept Form The slope-intercept form of the equation of the line with slope m and y-intercept 10, b2 is given as follows. y =mx +b EXAMPLE 3 Finding Slope and y-Intercept from an Equation of a Line Find the slope and y-intercept of the line with equation 4x + 5y = -10. SOLUTION Write the equation in slope-intercept form. 4x + 5y = -10 5y = -4x - 10 Subtract 4x. y = - 4 5 x - 2 Divide by 5. m b The slope is - 4 5, and the y-intercept is 10, -22. S Now Try Exercise 37.
RkJQdWJsaXNoZXIy NjM5ODQ=