Question

6. Match each equation with the slope m and y-intercept of its graph.

Answer 1

A line equation, in slope-intercept form, has the following format:

$y=mx+b$

Where 'm' represents the slope and 'b' the y-intercept.

To match the lines with its respectives slopes and intercepts, we can just rewrite all the equation in slope-intercept form and compare them.

Let's start with those already in slope intercept form.

The second line is:

$y=5-6x$

The slope is -6, and the y-intercept is (0, 5).

The third line is:

$y=\frac{5}{6}x+1$

The slope is 5/6, and the y-intercept is (0, 1).

Now, the first line and the fourth, we need to rewrite them in slope intercept form. Let's start with

$5x-6y=30$

Rewriting in slope intercept form we have

$\begin{gathered} 5x-6y=30 \\ -6y=-5x+30 \\ 6y=5x-30 \\ y=\frac{5}{6}x-5 \end{gathered}$

The slope is 5/6, and the y-intercept is (0, -5).

For the last one, we can just match with the remaining slope and intercept.

For the last one, The slope is 5/6, and the y-intercept is (0, -1).