Features of a graph

Question

Consider the equation . For each question, explain or show your reasoning.

1. If we graph the equation, what is the slope of the graph?
2. Where does the graph intersects the -axis?
3. Where does it intersects the -axis?

Answer 1

Solve for equation in y = mx + b form:

1.5x + 4.5y = 18

4.5y = -1.5x + 18

y = (-1.5x + 18) / 4.5 = (-1/3)x + 4

If we graph the equation, what is the slope of the graph?

slope = m = -1/3

Where does the graph intersects the y-axis (where x = 0)?

y = (-1/3)x + 4 = (-1/3)(0) + 4 = 4

y-intercept = (0,4)

Where does it intersects the x-axis (where y = 0)?

0 = (-1/3)x + 4

(-1/3)x = -4

x = -4(-3) = 12

x-intercept = (12,0)

Answer 2

solve for y in terms of x. then the slope is the coefficient of the x term

4.5y= -1.5x + 18

y = (-1.5/4.5)x + 18/4.5

slope of the graph is -1.5/4.5 = - 1/3

18/4.5 is the y-intercept, where the graph intersects the y-axis

18/4.5 = 6/1.5 = 4 or the point (0,4)

y=mx+b is the general form of a linear equation where m=slope and b = the y intercept

here b= 4, m= -1/3

set y = 0 and solve for x to get the x intercept

1.5x = 18

x = 18/1.5 =12 or the point (12,0)