Question

The equation has a positive slope and a negative
y-intercept.

• A. $y=-2x-3$
• B. $y=2-3x$
• C. $y=2+3x$
• D. $y=-2+3x$

Answer 1

The correct option is D $y=-2+3x$

We know that equation of the line with y-intercept of the value $b$ is,
$y=mx+b$

Here, $\text{m}$ represents the slope of the line.

Now, let us consider each of the options given.

In case of first option:
Given equation is $y=2+3x$.
Here, $m=3$ and $b=2$
So, it has both a positive slope and a positive y-intercept.

In case of second option:
Given equation is $y=-2+3x$.
Here, $m=3$ and $b=-2$
So, it has a positive slope and a negative y-intercept.

In case of third option:
Given equation is $y=-2x-3$.
Here, $m=-2$ and $b=-3$
So, it has both a negative slope and a negative y-intercept.

In case of fourth option:
Given equation is $y=2-3x$.
Here, $\text{m = -3 and b = 2}$
So, it has a negative slope and positive y-intercept.

$\therefore$ $y=-2+3x$ has a positive slope and a negative intercept.