# What is the equation of the graphed line in point-slope form? y – 1 = 2/3 (x + 3), y – 1 = 2/3 (x – 3), y + 1 = 2/3

###### Question:

## Answers

Hello!

First of all we need to find the slope. To do so we use the following equation.

[tex]\frac{ y_{2}- y_{1} }{ x_{2}- x_{1} }[/tex]

The ones and twos just represent different ordered pairs. We will have (-3,3) be ([tex]x_{1} , y_{1}[/tex]) and (3,1) be ([tex]x_{2} , y_{2}[/tex]) Now we plug our numbers into the formula.

[tex]\frac{1+3}{3+3} = \frac{4}{6} = \frac{2}{3}[/tex]

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Now we need to write our equation in point-slope form, which is y-k=m(x-h), where (h,k) represent a point on the line, and m is the slope.. We will use (3,1) for (h,k). Our final equation is shown below.

y-1= [tex]\frac{2}{3}[/tex](x+3)

I hope this helps!

(3,1)(-3,-3)

slope = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

y - y1 = m(x - x1)

slope(m) = 2/3

(3,1)x1 = 3 and y1 = 1

now sub

y - 1 = 2/3(x - 3) <===

b

Step-by-step explanation:

ANSWER

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

EXPLANATION

To find the equation in point-slope form, use the formula,

[tex]y-y_1=m(x-x_1)[/tex]

The [tex]m[/tex]

is the slope of the line.

We can read from the graph that, the straight line passes through, the points

[tex](-3,-3) \: and \: (3,1)[/tex]

We can use these two points to find the slope of the line.

The slope can found using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

This means that,

[tex]m = \frac{1 - - 3}{3 - - 3}[/tex]

[tex]m = \frac{1 + 3}{3 + 3}[/tex]

[tex]m = \frac{4}{6}[/tex]

[tex]m = \frac{2}{3}[/tex]

We now use one of the points, say

[tex](3,1)[/tex]

with the slope to find the equation of the line.

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

ANSWER

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

EXPLANATION

To find the equation in point-slope form, use the formula,

[tex]y-y_1=m(x-x_1)[/tex]

The [tex]m[/tex]

is the slope of the line.

We can read from the graph that, the straight line passes through, the points

[tex](-3,-3) \: and \: (3,1)[/tex]

We can use these two points to find the slope of the line.

The slope can found using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

This means that,

[tex]m = \frac{1 - - 3}{3 - - 3}[/tex]

[tex]m = \frac{1 + 3}{3 + 3}[/tex]

[tex]m = \frac{4}{6}[/tex]

[tex]m = \frac{2}{3}[/tex]

We now use one of the points, say

[tex](3,1)[/tex]

with the slope to find the equation of the line.

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

First you do the distributive property and then you have to use the inverse property of each equation and after all the math the answer is y-1= 2/3(x-3)

P.S: Next time you may want to add the fractions in the possible answers

Slope = 4/6= 2/3

Intercept is -1 (I think just check with gradient on graph in doing in my head)

Y=MX+B

Y=2/3X-1 ( if my calculations add up

We first need to find the gradient of the line

[tex]\frac{y_{2}- y_{1} } {x_{2}-x_{1} } = \frac{-3-1}{-3-3}= \frac{-4}{-6}= \frac{2}{3}[/tex]

From the graph, we see the graph intercepts y-axis at -1

Hence, the equation of the line is [tex]y= \frac{2}{3}x-1[/tex]