Find the slope-intercept form of the equation of a line that passes through the given points.
-$$( 9,0 ) , ( 0,3 )$$
A) $y = \frac { 1 } { 3 } x + 3$
B) $y = - 3 x + 3$
C) $y = - \frac { 1 } { 3 } x + 3$
D) $y = - \frac { 1 } { 3 } x - 3$

Question

Quizplus · Accepted Answer

We can use the slope-intercept form of the equation of a line, $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

First, we need to find the slope. Using the two given points, we can use the slope formula: 
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{0 - 9} = -\frac{1}{3}$$

Now that we know the slope, we can use one of the two given points and the slope to find the y-intercept, $b$. Using the point $(9,0)$:
$$0 = -\frac{1}{3}(9) + b \quad \Rightarrow \quad b = 3$$

Therefore, the equation of the line in slope-intercept form is:
$$y = -\frac{1}{3}x + 3$$

So the answer is choice C.

Find the Slope-Intercept Form of the Equation of a Line (9,0),(0,3)( 9,0 ) , ( 0,3 )(9,0),(0,3)

Find the Slope-Intercept Form of the Equation of a Line $( 9,0 ) , ( 0,3 )$