Graph the line having a slope of 1 3 \frac13 and passes through ( 4 , 3 ) \left(4,3\right) .

This problem asks us to graph a line having a slope of one third that passes through the point four three. So I notice that we are given a point, which is four three, and then we are also given our slope, which is one third. Now let's start by plotting our point. So this point is gonna be when x is four and y is three. As the x is four and then y is three, giving us this point on our graph. So we plotted the point four three. Now next, I need to find my slope to or or use my slope to find another point. Recall that slope is rise divided by run. I can see that my rise is positive one, so that means I'm going to be going up by one. And I can also see that my run is three, so that means I'm going to be going to the right three. But you might notice that we end up off of our graph. So what's something I can do, so that way we can get a point that's on our graph? Well, you could plot a point outside of this, and then try to create a line from here, but this is not gonna look very good. And if we need to plot a second point, there is a way we can go about doing this. One over three is the same thing as negative one over negative three. Now why would I write it like this? Well, notice that the negatives would cancel, and this would still just give us one third. But now, rather than rising one up, I'm gonna go down one, and then rather than going to the right three, I'm gonna go to the left three. So looking at my initial point, I can now go down by one and then to the left by three. And that's going to give me another point on my graph right about well, it's gonna be down to the yeah. Down to the left three, so right about that. So this point ends up at an x of one and a y of two. So we now have two points plotted on our graph, and all I need to do is connect these with a line and extend the line in both directions, which will give me the graph that I'm looking for. So this is how you can graph lines when you are given a slope and you are given a point.

4. Graphing

Slope of a Line

Beginning Algebra

4. Graphing

Slope of a Line

Struggling with Beginning Algebra?

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Multiple Choice

Graph the line having a slope of $\frac{1}{3}$ and passes through $open paren 4 comma 3 close paren$ .

Graph showing a line with slope -4 passing through the point (4, 3) on a coordinate plane.

Graph showing a line with slope 13 1/3 passing through the point (4, 3) on a Cartesian plane.

Graph showing a line with slope 13 1/3 passing through the point (4, 3) on a coordinate plane.

Graph of a line with slope 13 1/3 passing through point (4,3) on a coordinate plane with labeled axes.

Verified step by step guidance

Step 1: Identify the given slope and point. The slope is $\frac{1}{3}$ and the point the line passes through is $(4, 3)$.

Step 2: Use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the given point. Substitute $m = \frac{1}{3}$, $x_1 = 4$, and $y_1 = 3$ into the formula.

Step 3: Write the equation as $y - 3 = \frac{1}{3}(x - 4)$.

Step 4: To graph the line, start by plotting the point $(4, 3)$ on the coordinate plane.

Step 5: From the point $(4, 3)$, use the slope $\frac{1}{3}$ to find another point. Since the slope is rise over run, move up 1 unit and right 3 units from the point $(4, 3)$, then plot this second point. Draw a line through these two points to complete the graph.

5:13m

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Struggling with Beginning Algebra?

Graph the line having a slope of 13\(\frac\)13 and passes through (4,3)\(\left\)(4,3\(\right\)).

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Graph the line having a slope of $\frac{1}{3}$ and passes through $open paren 4 comma 3 close paren$ .