Question

For each linear function graphed on the coordinate grid, enter the value of m and the value of b. Give your answers as fractions in simplest form. 8 6 5 183 4 3 2 1 3 -3 - 3 -10 -98 lo S 910 f(x), red line: g(x), blue line: m= h(x), green line: m = Check Answer Next Question Question 6 of 8 POWER ? XKNEWTON ! Turn it in Save & Close O E e​

Answer 1

f(x), Red Line: m = -½; b = 2

g(x), Blue Line: m = ⅓; b = -1

h(x), Green Line: m = 3; b = 0

Step-by-sep explanation:

✍️Note the following:

✔️The slope of a line, m, =
`(rise)/(run) = (y_2 - y_1)/(x_2 - x_1)`

✔️y-intercept, b, = the point on the y-axis where the line intercepts the y-axis, and where x = 0.

f(x), Red Line:

Using 2 points on the red line, (6, -1) and (8, -2)

slope (m) =
`(y_2 - y_1)/(x_2 - x_1) = (-2 -(-1))/(8 - 6) = (-1)/(2)`

m = -½

The red line intercepts the y-axis at y = 2, therefore:

b = 2

g(x), Blue Line:

Using 2 points on the blue line, (0, -1) and (3, 0)

slope (m) =
`(y_2 - y_1)/(x_2 - x_1) = (0 -(-1))/(3 - 0) = (1)/(3)`

m = ⅓

The blue line intercepts the y-axis at y = -1, therefore:

b = -1

h(x), Green Line:

Using 2 points on the green line, (0, 0) and (1, 3)

slope (m) =
`(y_2 - y_1)/(x_2 - x_1) = (3 - 0)/(1 - 0) = (3)/(1) = 3`

m = 3

The green line intercepts the y-axis at y = 0, therefore:

b = 0.