The graph of linear function `g` passes through the points `\left(4,-1\right)`and `\left(-8,\ -4\right),`as shown. What are the slope and y-intercept of the graph `g`?

Answer 1

To find the slope of the graph, we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

Using the points (4, -1) and (-8, -4):

slope = (-4 - (-1)) / (-8 - 4)
slope = (-4 + 1) / (-12)
slope = -3 / -12
slope = 1/4

Now that we have the slope, we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)

Using the point (4, -1) and the slope 1/4:

y - (-1) = 1/4(x - 4)
y + 1 = 1/4x - 1
y = 1/4x - 2

Therefore, the slope of the graph `g` is 1/4 and the y-intercept is -2.