Question

Identify the values of m and b of the linear function y = mx + b, graphed below. ​

Answer 1

Finding the slope and y-intercept of a line given the graph

Answer:

`b = 4`

`m = -(1)/(3)`

Explanation:

An equation of a line written in its Slope-intercept Form,
`y = mx +b`, has
`b` as its
`y`-intercept and
`m` as its slope.

`b` or the
`y`-intercept is the
`y`-coordinate when
`x = 0`. On the given line, we can see that when
`x = 0`,
`y = 4`. It's
`y`-intercept is the point
`(0,4)` so
`b = 4`.

The slope,
`m`, of the line can be calculated by
`(y_2 -y_1)/(x_2 -x_1)\\` where
`x_n` and
`y_n` is the
`xy`-coordinates of any point
`n` on the line. In the given line, we can see that
`(5,3)` is on the line so this can be point
`1`.
`(0,4)` is also on the line (yes, you can also use the
`y`-intercept in calculating the slope of the line) so this can be our point
`2`.

`m = (4 -3)/(0 -3) \\ m = (1)/(-3) \\ m = -(1)/(3)`

The
`y`-intercept is
`b = 4` and the slope is
`m = -(1)/(3)`