Question

Which of the following graphs represents the equation y -4 =3 (x-1)

Answer 1

The line represented by the equation y - 4 = 3(x - 1) would have a slope of 3 and a y-intercept at the point (0, 1). It is different from the graphs described in the reference with a line of equation y = 9 + 3x which have a y-intercept at 9.

Step-by-step explanation:

The equation y - 4 = 3(x - 1) represents a line with a slope of 3, which means for every increase of 1 on the horizontal axis (x), there is a rise of 3 on the vertical axis (y). To find where this line crosses the y-axis (y-intercept), you would set x to 0 and solve for y. Substituting x with 0 gives you y - 4 = 3(0 - 1), which simplifies to y = 1. Therefore, the y-intercept is at the point (0, 1). The graph matching this equation would have a y-intercept at 1, not at 9 as described in the reference figures that show a different line, y = 9 + 3x, which has its y-intercept at 9. Therefore, none of the described graphs would represent the equation y - 4 = 3(x - 1).

Answer 2

To start, we can factor the "3" in the parentheses - then move the -4 over. So,

y - 4 = 3x - 3
y = 3x + 1

So the y-intercept of the equation is "1", and the slope is 3.