In the graph shown, identify the yy–intercept & slope. Write the equation of this line in Slope-Intercept form.

y = − 2 3 x + 1 y=-\frac23x+1 y = − 3 2 x + 1

In the graph shown, identify the y y –intercept & slope. Write the equation of this line in Slope-Intercept form.

Welcome back, everyone. So in this problem here, we're gonna identify the y intercept and slope of this line that's shown to us here. And we wanna do this because we wanna ultimately write the equation of this line in slope intercept form. Remember the equation of slope intercept form is just y equals mx plus b. So in order to figure out y equals mx plus b, I wanna write an equation like this. I have to figure out what these two variables are, m and b. So let's go do that. The easiest one to always start off with is the b term, the y intercept, because you're really just looking at the y axis. Remember, we're just trying to figure out what's the y value when this line crosses. And, basically, if you look, it's right over here and b equals 1. So really straightforward. You just look where the line is, and then that's your y intercept. Alright. So now to calculate the slope, the slope is a little bit more involved because we're basically gonna have to figure out the rise of the run between this point over here and one of the other points. So, for example, we see this line is going down to the right, so we can pick another point over here to calculate our slope. And if you keep looking over here as you keep going, this isn't gonna be a good line or, sorry, this is gonna be a good point because it's not sort of like the intersection of 2 points. It's, like, halfway. This point isn't good either. This point isn't good, but this one is because this point over here is intersecting between two lines. It's a clean number, so this is gonna be a good way to calculate my m. So let's go ahead and do this. So remember that m is just equal to delta y over delta x. Right? So change in y and change in x, rise over the run. Any way you could sort of think about that. Right? So in other words, from this point to this point, what's the rise over the run? Well, in in order to get from this point here, first, you have to go down, and I actually have to go down by 2, and then I have to go over by 3. And what happens is this has to be negative because I'm going down, and then if I'm going to the right, that stays positive. So, basically, what happens is that my delta y is equal to negative 2, but my delta x is equal to positive 3. So the rise of the run is negative 2 thirds, and that is equal to your m value. So now that we have m and b, we can write this equation in slope intercept form. And, basically, what this is gonna be, this is gonna be y equals negative 2 over 3 x. So it can be fractions, slopes can be fractions, and they could also be negative. That's perfectly fine. Plus and then y intercept of 1. This is how to describe this equation here that's shown to us in slope intercept form. So thank

In the graph shown, identify the y y –intercept & slope. Write the equation of this line in Slope-Intercept form.

y = − 2 3 x + 1 y=-\frac23x+1 y = − 3 2 x + 1

y = 2 3 x + 1 y=\frac23x+1 y = 3 2 x + 1

y = − 2 x + 1 y=-2x+1 y = − 2 x + 1

4. Graphing Linear Equations in Two Variables

Slope-Intercept Form

Beginning & Intermediate Algebra

4. Graphing Linear Equations in Two Variables

Slope-Intercept Form

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Multiple Choice

In the graph shown, identify the $y$ –intercept & slope. Write the equation of this line in Slope-Intercept form.

$y=\frac23x+1$

$y=-\frac23x+1$

$y=-2x+1$

$y=x+2$

Verified step by step guidance

Identify the y-intercept by looking at the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at $y = 1$.

Determine the slope by finding two points on the line. For example, use the points $(0, 1)$ (the y-intercept) and $(3, -1)$.

Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substitute the points: $m = \frac{-1 - 1}{3 - 0} = \frac{-2}{3}$.

Write the equation of the line in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Substitute the slope and y-intercept values into the equation: $y = -\frac{2}{3}x + 1$.

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