Question

I think I have the slope but I need help with the equation and the y-intercept

Answer 1

• 
  `m=(1)/(2)`

• The y-intercept (b) = -2

• The equation of the line is:

`y=(1)/(2)x-2`

Explanation:

Given the points

• (4, 0)

• (0, -2)

Finding the slope between two points

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

`\left(x_1,\:y_1\right)=\left(4,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-2\right)`

`m=(1)/(2)`

We know that the y-intercept can be obtained by setting the value x=0 and solving for y.

From the graph, it is clear that at x=0, the value of y = -2

Thus, the y-intercept (b) = -2

We know that the slope-intercept form of the line equation is

`y=mx+b`

where m is the slope and b is the y-intercept.

Substituting m=1/2 and y-interept (b) = -2 in the slope-intercept form of the line equation

`y=mx+b`

`y=(1)/(2)x+\left(-2\right)`

`y=(1)/(2)x-2`

Thus, the equation of the line is:

`y=(1)/(2)x-2`