EXAMPLE 4 Write an equation of a line

EXAMPLE 4 Write an equation of a line from a graph Gym Membership The graph models the total cost of joining a gym. Write an equation of the line. Explain the meaning of the slope and the y-intercept of the line. SOLUTION STEP 1 Find the slope. 363 – 231 = 44 m= 5– 2

EXAMPLE 4 Write an equation of a line from a graph STEP 2 Find the y-intercept. Use the slope and one of the points on the graph. y = mx + b Use slope-intercept form. 231 = 44 2 + b Substitute for x, y, and m. 143 = b Simplify. STEP 3 Write the equation. Because m = 44 and b = 143, an equation of the line is y = 44 x + 143.

EXAMPLE 5 Graph a line with equation in standard form Graph 3 x + 4 y = 12. SOLUTION The equation is in standard form, so you can use the intercepts. STEP 1 Find the intercepts. To find the x-intercept, let y = 0. 3 x +4 y = 12 3 x +4 ( 0 ) = 12 x=4 To find the y-intercept, let x = 0. 3 x +4 y = 12 3 ( 0 ) + 4 y = 12 y=3

EXAMPLE 5 Graph a line with equation in standard form STEP 2 Graph the line. The intercepts are (4, 0) and (0, 3). Graph these points, then draw a line through the points.

GUIDED PRACTICE 5. for Examples 4 and 5 The equation y = 50 x + 125 models the total cost of joining a climbing gym. What are the meaning of the slope and the y-intercept of the line? SOLUTION The equation y = 50 x + 125 models the cost. The slope is monthly fee, $50 , and the y- intercept is the initial cost to join the gym, $125.

GUIDED PRACTICE Graph the equation 6. 2 x – 3 y = 6 SOLUTION for Examples 4 and 5

GUIDED PRACTICE Graph the equation 7. y = 4 SOLUTION for Examples 4 and 5

GUIDED PRACTICE Graph the equation 8. x = – 3 SOLUTION for Examples 4 and 5