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:

$b = 4$

$m = -\frac{1}{3}$

Step-by-step 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 $\frac{y_2 -y_1}{x_2 -x_1}$ 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 $2$.

$m = \frac{4 -3}{0 -3} \\ m = \frac{1}{-3} \\ m = -\frac{1}{3}$

The $y$-intercept is $b = 4$ and the slope is $m = -\frac{1}{3}$