Question

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

Answer 1

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:

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

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

Answer 2

Answer:

Slope

$m=-\frac{3}{5}$

point-slope form

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

slope-intersection form

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

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 $b=1.8$