Write each equation in point-slope form.Slope: m=−32m=-\frac32; Point: (0,5)\left(0,5\right)

y − 5 = − 3 2 x y-5=-\frac32x y − 5 = − 2 3 x

Write each equation in point-slope form.Slope: m = − 3 2 m=-\frac32 ; Point: ( 0 , 5 ) \left(0,5\right)

this problem, we are asked to write each equation in point slope form. Now recall for, to write this in point slope form, it's gonna be this equation, y minus y one is equal to m times x minus x one. So So for point slope form, we need a slope and a point. Now I can see we have our slope, m, which is given in the problem right about here, and I can also see that we have a point right there. Now this point is going to be in the form x one y one, and so that's what we need for our x one and y one in this equation. So let's see if we can put this all together. So this is going to be y minus y one, where I can see that my y one is five. That's going to equal m, my slope, which I can see is negative three halves. That's going to be times x minus x one, which I can see is zero. So inserting our point and our slope, we get this as our equation. Now to make things simpler, I can drop these parentheses. So we're just gonna get y minus five is going to be equal to negative three halves. And notice here that we have x minus zero. X minus zero or anything minus zero is just gonna be whatever that thing is, so we're just gonna have x. So negative three halves x, and this right here would be our equation in point slope form. Hope you found this video helpful.

Write each equation in point-slope form. Slope: m = − 3 2 m=-\frac32 ; Point: ( 0 , 5 ) \left(0,5\right)

y − 5 = − 3 2 x y-5=-\frac32x y − 5 = − 2 3 x

y = − 3 2 ( x − 5 ) y=-\frac32\left(x-5\right) y = − 2 3 ( x − 5 )

y = 3 2 ( x − 5 ) y=\frac32\left(x-5\right) y = 2 3 ( x − 5 )

y + 5 = − 3 2 x y+5=-\frac32x y + 5 = − 2 3 x

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: $m = - \frac{3}{2}$ ; Point: $open paren 0 comma 5 close paren$

$y-5=-\frac32x$

$y=-\frac32\left(x-5\right)$

$y=\frac32\left(x-5\right)$

$y+5=-\frac32x$

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 and point from the problem: the slope $m = -\frac{3}{2}$ and the point is $(0, 5)$.

Substitute the slope $m = -\frac{3}{2}$ and the coordinates of the point $x_1 = 0$, $y_1 = 5$ into the point-slope formula: \[y - 5 = -\frac{3}{2}(x - 0)\]

Simplify the expression inside the parentheses: since $x - 0$ is just $x$, the equation becomes: \[y - 5 = -\frac{3}{2}x\]

This is the equation in point-slope form representing the line with slope $-\frac{3}{2}$ passing through the point $(0, 5)$.

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