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weeeeeb [17]
2 years ago
6

The equation of the graphed line in point-slope form is?, and it’s equation in slope-intercept form is?

Mathematics
2 answers:
nika2105 [10]2 years ago
8 0

Answer:

<u><em>Slope</em></u>

m=-\frac{3}{5}

<em><u>point-slope form </u></em>

y=-\frac{3}{5}(x-3)

<u><em>slope-intersection form </em></u>

y=-\frac{3}{5}x+1.8

Step-by-step explanation:

The equation of a line in the point-slope form has the following formula:

y-y_0 = m (x-x_0)

Where m is the slope and (x_0, y_0) is a point belonging to the line.

The equation of a line in the slope-intersection form has the following formula:

y = mx + b

Where b is the intersection of the line with the y axis.

To calculate the slope of the line knowing 2 points we use the following formula:

m=\frac{y_1-y_0}{x_1-x_0}

In this case:

x_0 =3\\y_0=0\\x_1=-2\\y_1=3

So

m=\frac{3-0}{-2-3}

m=-\frac{3}{5}

So the equation of a line in the point-slope form

y-0 =-\frac{3}{5}(x-3)

y=-\frac{3}{5}(x-3)

The equation of a line in the slope-intersection form is:

y-0=-\frac{3}{5}(x-3)

y=-\frac{3}{5}(x-3)

y=-\frac{3}{5}x+\frac{9}{5}

y=-\frac{3}{5}x+1.8

with b=1.8

tester [92]2 years ago
4 0

ANSWER

Point-slope form:

y - 3 =  -\frac{3}{5} (x  + 2)

Slope-intercept form:

y= -\frac{3}{5} x  +  \frac{9}{5}

EXPLANATION

The graphed line passes through

(-2,3) \:  \: and \:  \:  (3,0)

The slope of this line is determined using

m = \frac{y_2-y_1}{x_2-x_1}

We substitute the points to get;

m =  \frac{0 - 3}{3 -  - 2}

m = -\frac{3}{5}

The point-slope formula is:

y-y_1 = m(x - x_1)

Substitute the first point and slope to get:

y - 3 = -\frac{3}{5} (x -  - 2)

y - 3 = -\frac{3}{5} (x  + 2)

To find the slope-intercept form, we expand to get:

y= -\frac{3}{5} x  -  \frac{6}{5}  + 3

y= -\frac{3}{5} x  +  \frac{9}{5}

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