Question

Write an equation for the line graphed?

Answer 1

The equation of the line is:

y = 2/3x - 3

The graph is also attached below.

Explanation:

From the given diagram, let us take two points

(0, -3)

(4.5, 0)

Determining the slope between (0, -3) and (4.5, 0)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0,\:-3\right),\:\left(x_2,\:y_2\right)=\left(4.5,\:0\right)`

`m=(0-\left(-3\right))/(4.5-0)`

`m\:=(3)/(4.5)`

`m=(3)/((45)/(10))`

`m=(3\cdot \:10)/(45)`

`m=(2)/(3)`

Therefore, the slope of the line is:

m = 2/3

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the given point

• (0, -3)

It is clear that at x = 0, the value of y = -3

Thus, the y-intercept b = -3

now substituting b = -3 and m = 2/3 in the slope-intercept form of the line equation

y = mx+b

y = 2/3x + (-3)

y = 2/3x - 3

Therefore, the equation of the line is:

y = 2/3x - 3

The graph is also attached below.