Question

Find an equation for the line of, (-5, -4) and (-1, 4). Write the answer in slope-intercept form.

Answer 1

y=2x+6

Step-by-step explanation:

Given any two points on a line, to find the equation of the line, we can use the two-point form of the equation of a line stated below.

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

If the points are:

`\mleft(x_1_{},y_1\mright)=\mleft(-5,-4\mright),(x_2,y_2)=(-1,4)`

Substitute into the formula:

`\begin{gathered} (y-(-4))/(x-(-5))=(4-(-4))/((-1)-(-5))\implies(y+4)/(x+5)=(4+4)/(-1+5)=(8)/(4) \\ \implies(y+4)/(x+5)=2 \end{gathered}`

Next, we write it in the slope-intercept form:

`\begin{gathered} y+4=2(x+5) \\ y=2x+10-4 \\ y=2x+6 \end{gathered}`

The equation of the line is y=2x+6.