Question

Find the slope, starting point and equation of each of the graphs

Answer 1

From the graph

The line passing through points (-1, 4) and (4, -4)

We will use these points to find the slope of the line

The rule of the slope is

`m=(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} x_1=-1 \\ y_1=4 \\ x_2=4 \\ y_2=-4 \end{gathered}`

Let us substitute these values in the rule

`m=(-4-4)/(4-(-1))=(-8)/(5)=-1.6`

The form of the equation is

y = m x + b

m is the slope

b is the y-intercept

Substitute m by -1.6

y = -1.6 x + b

To find b substitute x and y by the coordinates of a point on the line

x = -1 , y = 4

4 = -1.6(-1) + b

4 = 1.6 + b

Subtract 1.6 from both sides

4 - 1.6 = 1.6 - 1.6 + b

2.4 = b

Substitute the value of b in the equation

y = -1.6 x + 2.4

The slope = -1.6

y-intercept = 2.4

Equation : y = -1.6 x + 2.4