huda wrote:
In the xy-plane, what is the y-intercept of the line that passes through the point (1, −2) and has an x-intercept of 3?
A. 1
B. 0
C. −1
D. −2
E. −3
Key concept: If the line has x-intercept 3, then the line crosses the x-axis at the point (3, 0)So we now know that two points on the line are (1, -2) and (3, 0)
Our goal will be to find the equation of the line in slope y-intercept form,
y = mx + b, where m is the slope of the line and b is the y-intercept
The slope between the two points = m = rise/run = (0 - -2)/(3 - 1) = 2/2 = 1
Now that we know the slope = 1, we know that the equation of the line is
y = 1x + bAt this point we can find the value of b by plugging in the coordinates of one point on the line.
Since (3, 0) is on the line, we can plug x = 3 and y = 0 into the equation to get 0 = 1(3) + b
When we solve this equation for b, we get: b = -3
So the equation of the line is
y = x - 3, which means the y intercept (aka b) is -3
Answer: E
Cheers,
Brent