Q27. - Algebra 2

Question

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

$\text{ x}-\text{intercept 9, }y-\text{intercept -4}$

Step-by-Step Solution

Answer

The equation of the line in slope intercept having x- intercept as 9 and y-  intercept as -4 is $y=\frac{4}{9}x-4$.

Step-1 – Apply the concept of slope-intercept form of a linear equation

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ where $x_1\ne x_2$.

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

Step-2 – Find the ordered pairs

Given that x-intercept is 9. By x-intercept, it means that the y- coordinate is 0. Therefore from x-intercept the ordered pair (9,0) is obtained. Also given that the  y-intercept is -4 and this means that the x-coordinate is 0. Therefore from the y-intercept, the ordered pair (0,-4) is obtained.

Step-3 – Find the value of slope

From the points $\left(9,0\right)\text{ and }\left(0,-4\right)$ in the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$, the slope is obtained as

$\begin{array}{c}m=\frac{-4-\left(0\right)}{0-9}\\ =\frac{-4}{-9}\\ =\frac{4}{9}\end{array}$

Hence the slope is $\frac{4}{9}$

Step-4 – Find the equation in Slope-intercept form

By using the value of slope and y-intercept in the $y=mx+b$, the equation of line in slope intercept form is obtained as

$\begin{array}{c}y=\frac{4}{9}x+(-4)\\ y=\frac{4}{9}x-4\end{array}$

Hence the equation of line in slope intercept form is $y=\frac{4}{9}x-4$