Question

Identify the slope and y-intercept of the linear equation. X=0 M: B:X = -15. M: B:Y = 10x/3 + 19 M: B:

Answer 1

A line can be written in slope-intercept form, which is:

$y=mx+b$

where m represents the slope and b the y-intercept.

If we compare the third equation

$y=\frac{10}{3}x+19$

with the slope-intercept form, we have the slope and y-intercept:

$\begin{cases}m={\frac{10}{3}} \\ b={19}\end{cases}$

The slope of a line is a measure of its steepness. The lines:

$x=0\:and\:x=-15$

are both horizontal lines, therefore, the slope is undefined for both of them. The y-intercept is the point where the graph crosses the y-axis. One of the lines is the y-axis, therefore, it "cuts" the y-axis on every single point. The other line is just parallel to the y-axis, therefore, there's no y-intercept.

$\begin{gathered} x=0\implies\begin{cases}m={undefined} \\ b={y}\end{cases} \\ x=-15\implies\begin{cases}m={undefined} \\ b\in{\varnothing}\end{cases} \end{gathered}$