Question

Trying to help my daughter and it’s been years (I graduated in 98)

Answer 1

The form of the linear equation is

`y=mx+b`

m is the slope of the line of the equation

b is the y-intercept (value of y at x = 0)

The rule of the slope of the line which passes through points (x1, y1) and (x2, y2) is

`m=(y_2-y_1)/(x_2-x_1)`

Since the line passes through points (-3, 1) and (4, 8), then

Let (x1, y1) = (-3, 1) and (x2, y2) = (4, 8), then

`\begin{gathered} x_(_1)=-3,x_2=4 \\ y_1=1,y_2=8 \end{gathered}`

Substitute them in the rule of m above

`\begin{gathered} m=(8-1)/(4-(-3)) \\ m=(7)/(4+3) \\ m=(7)/(7) \\ m=1 \end{gathered}`

Now, substitute m by 1 in the form of the equation

`\begin{gathered} y=(1)x+b \\ y=x+b \end{gathered}`

We need to find the value of b, to do that we will use the point (4, 8)

Substitute x by 4 and y by 2 in the equation

`\begin{gathered} x=4,y=8 \\ 8=4+b \end{gathered}`

Subtract 4 from both sides to find b

`\begin{gathered} 8-4=4-4+b \\ 4=b \end{gathered}`

Substitute b by 4 in the equation

`y=x+4`

The equation of the line is y = x + 4

Answer B