Question

I am struggling with Linear Equations badly. I used the formula y=mx+b and I'm getting the right answer but it's asking me to put it x= instead of y= and I'm getting it wrong.Give the equation of the line passing through the each of the following pairs of points. Give your answers as equations in slope-intercept form, if appropriate, using fractions or integers. Otherwise use " x= The line passing through (-7,7) and (14,-2) has the equation

Answer 1

The general slope-intercept equation of a line is:

`y=m\cdot(x-x_1)+y_1\text{.}`

Where:

• m is the slope of the line,

,

• (x1, y1) are the coordinates of one point of the line.

The slope of the line can be computed by the following formula:

`m=(y_2-y_1)/(x_2-x_1)\text{.}`

Where (x1, y1) and (x2, y2) are coordinates of two points of the line.

In this problem, we have a line that passes through the points:

• (x1, y1) = (-7, 7),

,

• (x2, y2) = (14, -2).

Replacing the data of the points in the equation of m, we get:

`m=(-2-7)/(14-(-7))=-(9)/(21)=-(3)/(7)\text{.}`

Replacing m = -3/7 and (x1, y1) = (-7, 7) in the general equation of the line, we have:

`y=-(3)/(7)\cdot(x+7)+7.`

We can rewrite this equation in the following way:

`\begin{gathered} y-7=-(3)/(7)\cdot(x+7), \\ -(7)/(3)\cdot(y-7)=x+7, \\ x=-(7)/(3)\cdot(y-7)-7. \end{gathered}`

Answer

The equation of the line is:

`\begin{gathered} x=-(7)/(3)\cdot(y-7)-7 \\ x=-(7)/(3)\cdot(y+2)+14 \end{gathered}`