Question

Find the slope and y-intercept that has infinite solutions to the equation Click Here for Help Video

−
6
𝑥
+
3
𝑦
=
46
−6x+3y=46

The slope would be
.

The y-intercept would be
. (Do not list as a coordinate point.)

Answer 1

To find the slope and y-intercept of the equation \( -6x + 3y = 46 \) that has infinite solutions, we first need to rewrite the equation in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the original equation:

\[
-6x + 3y = 46
\]

We will solve for \( y \):

1. Add \( 6x \) to both sides:

\[
3y = 6x + 46
\]

2. Divide each term by \( 3 \):

\[
y = 2x + \frac{46}{3}
\]

Now we can identify the slope and y-intercept:

- The slope \( m \) is \( 2 \).
- The y-intercept \( b \) is \( \frac{46}{3} \).

Thus:

- The slope would be \( 2 \).
- The y-intercept would be \( \frac{46}{3} \).