Q39. - Algebra 2

Question

Write an equation in slope-intercept form of the line that passes through the points.

(-1, -5), (1, 1), (3, 7)

 

Step-by-Step Solution

Answer

The equation of the required straight line in slope-intercept form is $y=3x-2$.

Step 1 – State the concept

The slope intercept form of a straight-line equation is $y=mx+c$ where $m$is the slope and $c$ is the y-intercept.

 The slope of a line passing through $\left(a,b\right)$ and $\left(c,d\right)$ is $m=\frac{d-b}{c-a}$.

 The equation of a straight-line having slope $m$ and passing through the point $\left(h,k\right)$ is given as $y-k=m\left(x-h\right)$.

Step 2 – List the given data

It is clear, from the given table, that the line passes through the points, $\left(-1,-5\right)$, $\left(1,1\right)$ and $\left(3,7\right)$.

Then, let $\left(h,k\right)=\left(-1,-5\right)$, $\left(a,b\right)=\left(1,1\right)$ and $\left(c,d\right)=\left(3,7\right)$.

Step 3 – Determine the slope

Put $\left(a,b\right)=\left(1,1\right)$ and $\left(c,d\right)=\left(3,7\right)$ in $m=\frac{d-b}{c-a}$ to get,

$\begin{array}{l}m=\frac{7-1}{3-1}\\ =\frac{6}{2}\\ =3\end{array}$

So, $m=3$

 So, the slope of the required line is $3$.

Step 4 – Write the equation

Put $m=3$ and $\left(h,k\right)=\left(-1,-5\right)$ in $y-k=m\left(x-h\right)$ to get,

 $y-\left(-5\right)=3\left(x-\left(-1\right)\right)$

 $y+5=3\left(x+1\right)$  (Simplify)

 $y+5=3x+3$  (Distributive property)

 $y+5-5=3x+3-5$   (Subtract 5 from both sides)

 $y=3x-2$   (Simplify)

 So, the required equation of the straight line in slope-intercept form is $y=3x-2$