Write each equation in point-slope form.Slope: m=13m=\frac13; Point: (−2,4)(−2,4)

y − 4 = 1 3 ( x + 2 ) y-4=\frac13\left(x+2\right) y − 4 = 3 1 ( x + 2 )

Write each equation in point-slope form. Slope: m = 1 3 m=\frac13 ; Point: ( − 2 , 4 ) (−2,4)

this problem, we are asked to write each equation in point slope form. Now recall that point slope form looks like this. It's going to be y minus y one is equal to m times x minus x one. Now to put together this equation, we first need to figure out what our slope is, and I can see that our slope is given to us as one third in this problem. And we're also going to need a point, and our point is going to be our x one, y one. Well, I can see that that point is given to us right here as negative two, four. So that means that our x one is going to be negative two, and our y one is going to be four. So we have the point, we have a slope. Now we can use point slope form. So let's do this, we're going to have y minus y one, and y one is going to be this four. And that's going to equal our slope, which I can see is one third. It's gonna be times x minus x one. We're gonna see x one is this negative two. So we now have point slope form put together, and I can go ahead and drop these parentheses and also cancel the negatives to get a positive. So we get y minus four is equal to one third times x plus two, and this would be point slope form and the solution to this problem. Hope you found this video helpful.

Write each equation in point-slope form. Slope: m = 1 3 m=\frac13 ; Point: ( − 2 , 4 ) (−2,4)

y − 4 = 1 3 ( x + 2 ) y-4=\frac13\left(x+2\right) y − 4 = 3 1 ( x + 2 )

y − 4 = 1 3 ( x − 2 ) y-4=\frac13\left(x-2\right) y − 4 = 3 1 ( x − 2 )

y − 1 3 = 4 ( x + 2 ) y-\frac13=4\left(x+2\right) y − 3 1 = 4 ( x + 2 )

y − 1 3 = 4 ( x − 2 ) y-\frac13=4\left(x-2\right) y − 3 1 = 4 ( x − 2 )

4. Graphs and Functions

Point Slope Form

Intermediate Algebra

4. Graphs and Functions

Point Slope Form

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Multiple Choice

Write each equation in point-slope form.

Slope: $m = \frac{1}{3}$ ; Point: $open paren negative 2 comma 4 close paren$

$y-4=$\frac$13$\left$(x-2$\right$)$

$y-4=$\frac$13$\left$(x+2$\right$)$

$y-$\frac$13=4$\left$(x+2$\right$)$

$y-$\frac$13=4$\left$(x-2$\right$)$

Verified step by step guidance

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

Identify the given slope $m = \frac{1}{3}$ and the given point $(-2, 4)$. Here, $x_1 = -2$ and $y_1 = 4$.

Substitute the slope and the coordinates of the point into the point-slope formula: \[y - 4 = \frac{1}{3}(x - (-2))\].

Simplify the expression inside the parentheses by changing the subtraction of a negative number to addition: \[y - 4 = \frac{1}{3}(x + 2)\].

This is the equation in point-slope form representing the line with slope $\frac{1}{3}$ passing through the point $(-2, 4)$.

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Struggling with Intermediate Algebra?

Write each equation in point-slope form.Slope: m=13m=\(\frac\)13; Point: (−2,4)(−2,4)

Watch next

Write each equation in point-slope form.

Slope: $m = \frac{1}{3}$ ; Point: $open paren negative 2 comma 4 close paren$