Using Graphs of Equations

• x & y intercepts •real world situation, write equations

x & y intercepts

x-intercept y-intercept

Y-intercept (0,-2) X-intercept (2,0) The x-intercept is the x coordinate of the point where the line crosses the x axis

Finding Intercepts

y-intercept (0,3) x-intercept (1,0)

Finding Intercepts from an equation • To find the y-intercept, Let x =0 then solve the remaining equation for y.

Solution (0,b) 5x + 4y = 20 5(0)+4y = 20 0 + 4y = 20 4y = 20 y = 5 Solution ( 0,5)

Finding Intercepts from an equation • To find the x-intercept, Let y =0 then solve the remaining equation for x.

5x + 4y = 20 5x+4(0) = 20 5x + 0 = 20 5x = 20 x = 4 Solution ( 4,0)

Finding Intercepts from an equation • To find the y-intercept, Let x =0 then solve the remaining equation for y.

Solution (0,b) 4x- y = 8 4(0) - y = 8 0-y = 8 -y = 8 y = -8 Solution ( 0, -8)

Finding Intercepts from an equation • To find the x-intercept, Let y =0 then solve the remaining equation for x.

4x – y = 8 4x – 0 = 8 4x = 8 x = 2 Solution ( 2,0)

Finding Intercepts from an equation x-intercept 3x – 5y = 30 3x – 5(0) = 30 3x – 0 = 30 3x = 30 x = 10 Solution (10,0) y-intercept 3x – 5y = 30 3(0) – 5y = 30 0 – 5y = 30 -5y = 30 y = -6 Solution (0,-6)

Graphing a line using x & y intercepts 2x + 3y = 6 y- intercept (0,2) x-intercept (3,0) Draw the line

Real World Situations

A restaurant pays you $20 for a four hour shift. You average $7.00 per table in tips. Write and graph an equation representing your total earnings per table in a shift x - # of tables y- total earnings total earnings = earn at tables + nightly wage y = 7x + 20

Real World Situations

Sasha burns 15 calories per minute rowing vigorously, but only 3 calories per minute rowing leisurely. If Sasha burned a total of 300 calories, how many minutes of each intensity did she row?

x - # of min rowing vigorously y - # of min rowing leisurely 15x + 3y = 300

Real World Situations

You have $4.00 in coins of dimes and quarters. How many of each type of coin do you have?

x – # of quarters y – # of dimes amt in quarters+ amt in dimes = total amt .25x + .10y = 4.00