Question

Graph a line trough the given point with the given slope. Point:(4, 4) slope ( -4/3

Answer 1

Given:

point =(4,4) slope(m)=-4/3

x₁=4 y=4

We find the intercept

substitute into y=mx + b

4=4(-4/3)+ b

4 = -16 /3 + b

4+16/3 = b

`(12+16)/(3)=b`
`b=(28)/(3)`

The equation can be form by substituting the value of m and b into y=mx+b

`y=-(4)/(3)x+(28)/(3)`

To be able to sketch the graph, we need two points, the x and y-intercept.

To find the y-interpet, substitute x=0 into the equation

y = 28/3

Hence, the y-intercept is (0, 9.3)

To find the x-intercept, put y=0 and solve for x

`\begin{gathered} 0=-(4)/(3)x+(28)/(3) \\ \\ (4)/(3)x=(28)/(3) \\ \\ x=(28)/(3)*(3)/(4) \\ x=(28)/(4) \end{gathered}`

The x-intercept is (7,0)

So we can now sketch the graph