Question

Tayler claims that when a linear equation is written in general form, Ax + By+ C = 0, the

x-intercept of the corresponding graph is always -(C/A)


a)Show that Tayler’s claim is true for the equation 3x+5y+ 45 = 0

b. Explain why -(C/A) represents the x-intercept. (Hint: What y-value can be substituted into Ax +By+ C = 0 to determine the x-intercept?)

c. Tayler’s claim is not true for horizontal lines. Explain why.

d. Suggest a similar rule for the y-intercept. Check the rule using 3x+5y+ 45 = 0.

Answer 1

Ax + By + C = 0
A. 3x + 5y + 45 = 0
3x + 5(0) + 45 = 0
3x = -45
x = -45/3......x int.....-C/A
x = -15

B. To find the x intercept, u must sub in 0 for y and solve for x

C. This is not true for a horizontal line because u can't sub in 0 for x because a horizontal line never crosses the x axis and therefore, does not have an x axis.

D. y int is -C/B....u find this by subbing in 0 for x and solving for y
3x + 5y + 45 = 0
3(0) + 5y + 45 = 0
5y = -45
y = -45/5......y int = -C/B
y = -9