Question

find the slope of the graph write it as a fraction or whole number not a mixed number. find two points on the line (0,-4) and (3,0) slope = change in y / change in x

Answer 1

The slope of the graph will be:

• 
  `m=(4)/(3)`

From the attached graph, it is clear that

• the y-intercept is: (5, 0) ∵ to find the y-intercept, set x=0

• the x-intercept is: (0, -4) ∵ to find the x-intercept, set y=0

Explanation:

Given the two points on the line

• (0, -4)

• (3, 0)

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0,\:-4\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right)`

`m=(0-\left(-4\right))/(3-0)`

`m=(4)/(3)`

Hence, the slope of the graph will be:

`m=(4)/(3)`

We can also find the equation of the line using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

substituting the values m = 4/3 and the point (0, -4)

`y-\left(-4\right)=(4)/(3)\left(x-0\right)`

`y+4=(4)/(3)\left(x-0\right)`

`y+4=(4)/(3)x`

`y=(4)/(3)x-4`

Therefore, the equation of the line will be:

`y=(4)/(3)x-4`

The graph of the equation line is also attached below.

From the graph, it is clear that

• the y-intercept is: (5, 0) ∵ to find the y-intercept, set x=0

• the x-intercept is: (0, -4) ∵ to find the x-intercept, set y=0