Q57. - Algebra 2

Question

Write an equation in slope-intercept form that satisfies each set of conditions.

Passes through$(0,-2)$ and$(4,2)$.

Step-by-Step Solution

Answer

The equation in slope-intercept form is $y=x-2.$

Step-1 –Point slope equation of a line.

The point slope form of a straight line in geometry is used to represent the equation of a straight line using its slope ‘m’ and a point $(x,y)$ that lies on the line$y-y_1=m(x-x_1)$.

Step-2 – Determine the given value.

The line passes through$(0,-2)$ and$(4,2).$

Thus, $\left[\right(x_1,y_1)=(0,-2)$,and$(x_2,y_2)=(4,2)]$

Step-3 – Determine the equation

Slope of the line.

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-(-2)}{4-0}\\ m=1\end{array}$

Equation of the line for slope $m=1$ and points$(4,2).$

$\begin{array}{l}y-y_1=m(x-x_1)\\ y-2=1(x-4)\\ y-2=x-4\\ y=x-2\end{array}$

Therefore, the equation in slope-intercept form is$y=x-2.$