Question

Answer the following questions for the graph at right.a. What is the slope of the line? _____b. What is the y-intercept? (___ , ___)c. Find the slope of each line below.

Answer 1

To get the slope, intercept, and equation of the line

Step 1: We can select two points on the line to get the slope

let's pick points (0,4) and (-2,0)

`\text{slope }=\frac{0\text{ - 4}}{-2\text{ - 0}}=(-4)/(-2)=2\text{ }`

Slope = 2

Step 2: The y-intercept is the point on the line that cuts the y-axis

From the graph, the y-intercept is (0,4)

The x-intercept is the point on the line that cuts the x-axis

From the graph, the x-intercept is (-2,0)

Step 3: picking the points (0,4) and (-2,0)

we can use the formula

`\text{slope =}(y-y_1)/(x-x_1)=\text{ }(y_2-y_1)/(x_2-x_1)`

`\begin{gathered} \frac{y\text{ -4}}{x-0}=\text{ }(0-4)/(-2-0) \\ \\ (-4)/(-2)\text{ =}\frac{y\text{ - 4}}{x\text{ - 0}} \end{gathered}`

`\begin{gathered} 2\text{ =}\frac{y\text{ - 4}}{x} \\ \end{gathered}`

Cross multiplying

2x = y - 4

Re-writing

y = 2x + 4

Equation of the line is

y = 2x + 4