QuestionFind the slope and $y$ -intercept of the line. $-2 x-3 y=-6$

Studdy Solution

STEP 1

What is this asking? We're looking for the slope and y-intercept of a line given its equation in standard form! Watch out! Don't mix up the x and y intercepts!
Also, remember the slope is the number multiplying x when the equation is in slope-intercept form.

STEP 2

1. Rewrite the equation
2. Identify slope and y-intercept

STEP 3

We want to rewrite the equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
To do this, we first isolate the y term.
Let's add $2x$ to both sides of the equation $-2x - 3y = -6$ : $-2x - 3y + 2x = -6 + 2x$ $-3y = 2x - 6$

STEP 4

Now, we divide both sides by $-3$ to get y by itself: $\frac{-3y}{-3} = \frac{2x - 6}{-3}$ $y = \frac{2x}{-3} + \frac{-6}{-3}$ $y = -\frac{2}{3}x + 2$ Now our equation is in slope-intercept form!

STEP 5

Remember, the slope-intercept form is $y = mx + b$ , where $m$ is the slope.
Looking at our equation $y = -\frac{2}{3}x + 2$ , we can see that the slope $m$ is $-\frac{2}{3}$ .

STEP 6

In the slope-intercept form $y = mx + b$ , $b$ represents the y-intercept.
In our equation $y = -\frac{2}{3}x + 2$ , the y-intercept is $2$ .
This means the line crosses the y-axis at the point $(0, 2)$ .

STEP 7

The slope of the line is $-\frac{2}{3}$ and the y-intercept is $2$ .

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