Question

Which equation has an x-intercept of 3 and a y-intercept of -4 ?

y=3x-4 6x-8=24
y=-4x+3
8x-6y=24

Answer 1

The equation with an x-intercept of 3 and a y-intercept of -4 is y = 3x - 4. It meets the criteria since when x = 0, y = -4, and when y = 0, the equation resolves to x = 3.

Step-by-step explanation:

The student asked which equation has an x-intercept of 3 and a y-intercept of -4. To have a y-intercept of -4, the equation must intersect the y-axis at (0, -4). For an x-intercept of 3, the line must intersect the x-axis at (3, 0).

Looking at the given equations:

1. y = 3x - 4 matches our criteria directly. When x = 0, y = -4 (y-intercept), and when y = 0, x = 3 (solving the equation for x gives us the x-intercept).
2. 6x - 8 = 24 simplifies to y = 6x - 8 after dividing every term by 6, which does not provide the correct intercepts.
3. y = -4x + 3 has a y-intercept of 3, which is not what we are looking for.
4. 8x - 6y = 24 can be written in slope-intercept form as y = ⅓x - 4, which has a y-intercept of -4 but the x-intercept is not 3.

So, the correct equation is y = 3x - 4.