Write the point-slope form of the equation of a line with a slope of −25-\frac25−52 that passes through (1, 3). Then graph the equation.

y−3=−25(x−1)y-3=-\frac25\left(x-1\right)y−3=−52(x−1)

Write the point-slope form of the equation of a line with a slope of − 2 5 -\frac25 − 5 2 that passes through (1, 3) . Then graph the equation .

Hey, everyone. Let's take a look at this practice problem. Hopefully, you got a chance to try it on your own. So we're given some information about a line. We're told that it has a slope of negative 2 5ths, and it passes through a point 1 comma 3. So in other words, I know that the slope, which is m, is negative 2 over 5, and I also know that it passes through the point 1 comma 3. So what I wanna do is I wanna wanna write the point slope form of this equation of this line, and then I'm gonna go ahead and graph it. So let's get started. Remember that the point slope form is really just this formula over here. We've got y minus y one equals m parenthesis x minus x one. And, really, what happens in these types of problems is it's gonna give you a lot of the information that you already need plug into these this this equation. So for example, I need the m, but the m is already given to me. I'm told that the slope is negative 2 5ths, so that just pops straight into that equation. And then the other terms, like the y one and the x one, are really just the coordinates of the point that it's telling you it passes through. So, for example, this 1 comma 3, this is just gonna be your x one, and the 3 is gonna be your y one. So, really, it's already giving you everything that you need to actually write this equation in point slope form. We just basically replace the x one with 1, the y one with 3. Alright? So what this equation really just turns out to be is it just turns out to be y minus 3. Right? That's the y one coordinate equals m, in this case, which is negative 2 over 5. Right? That's the slope. And then x minus x1, and the x one is just 1. Now remember, just this y over here and this x are variables. We don't replace them with numbers, but that's really all there is to it. Right? So this is the equation of this line. It's in point slope form. So we're basically done with this. Right? The problem just gives you everything you need. You don't have to go calculate anything. Just sort of plug and shrug straight into this equation. So that's basically it. Now we're gonna go ahead and just graph it. And graphing is pretty straightforward because we're already told at least one of the points that it passes through. So, for example, it passes through the point 1 comma 3, which is over here. So it passes through this point, But how do you build the rest of the equation? Well, you're just gonna have to look at the slope, the rise over the run. We're told that the slope is negative 2 5ths. What that means is that you have to go down 2. That's the rise, and then you have to go over 5, that's the run. So the next point in your line is gonna be over here. You could also go up to like this and then to the left, 5, 1, 2, 3, 4, 5. That's gonna be over here, negative 5. And so these are gonna be your 3 points. So if you sort of build the line or sort of connect all these points over here, you're gonna see that your line is gonna look something like that. Alright? So that's the equation of this line, and that's also the graph of this line. Thanks for watching. Let me know if you have any questions.

Write the point-slope form of the equation of a line with a slope of −25-\frac25−52 that passes through (1, 3). Then graph the equation.

y−3=−25(x−1)y-3=-\frac25\left(x-1\right)y−3=−52(x−1)

y+3=25(x+1)y+3=\frac25\left(x+1\right)y+3=52(x+1)

y=−25x−1y=-\frac25x-1y=−52x−1

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Multiple Choice

Write the point-slope form of the equation of a line with a slope of $-$\frac$25$ that passes through (1, 3). Then graph the equation.

$y-3=-$\frac$25$\left$(x-1$\right$)$

$y-3=x-1$

$y+3=$\frac$25$\left$(x+1$\right$)$

$y=-$\frac$25x-1$

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Verified step by step guidance

Identify the point-slope form of a line equation, which is given by: $ y - y_1 = m(x - x_1) $, where $ m $ is the slope and $ (x_1, y_1) $ is a point on the line.

Substitute the given slope $ m = -\frac{5}{2} $ and the point $ (1, 3) $ into the point-slope form equation. This gives: $ y - 3 = -\frac{5}{2}(x - 1) $.

To graph the equation, start by plotting the point $ (1, 3) $ on the coordinate plane, as this is a point through which the line passes.

Use the slope $ -\frac{5}{2} $ to find another point on the line. From $ (1, 3) $, move down 5 units and right 2 units to find the next point.

Draw a line through the points $ (1, 3) $ and the new point you found using the slope. This line represents the graph of the equation $ y - 3 = -\frac{5}{2}(x - 1) $.