To find the x-intercept of a line, we need to find the value of x when y equals 0.
For f(x), the x-intercept is when y equals 0. We can set y equal to 0 in the equation of the line and solve for x:
0 = mx + b
0 = m(p) + b [since the x-intercept is (p,0)]
0 = mp + b
b = -mp
Now we can substitute the coordinates of the point (0,9) into the equation to find the value of m:
9 = m(0) + b
9 = 0 + b
b = 9
So the equation of f(x) is y = mp + 9. Substituting the coordinate (-4,6) into the equation:
6 = m(-4) + 9
6 = -4m + 9
-3 = -4m
m = 3/4
Therefore, the equation of f(x) is y = (3/4)x + 9.
Using the same process for g(x), we can find the equation of g(x) to be y = (2/7)x + 6.
To find the x-intercepts of f(x) and g(x), we can set y equal to 0 and solve for x:
0 = (3/4)x + 9
(3/4)x = -9
x = -36/3
x = -12
So the x-intercept of f(x) is (-12,0).
0 = (2/7)x + 6
(2/7)x = -6
x = -42/2
x = -21
So the x-intercept of g(x) is (-21,0).
Therefore, p + q = -12 + (-21) = -33.
Suppose the x
-intercept of f(x) is (p,0) and the x
-intercept of g(x) is (q,0) . What is the value of p+q
?
Two lines are graphed on a four quadrant coordinate plane. The x-axis and the y-axis go from negative 10 to 10 in increments of 1. One line, labeled f left parenthesis x right parenthesis, passes through (negative 4, 6) and (0, 9). The other line, labeled g left parenthesis x right parenthesis, passes through (negative 7, 6) and (0, 4).
(1 point)
Responses
−1
negative 1
1
1
0
0
2
1 answer