Question

find an equation of the line in the form ax + by = c whose x - intercept is 18 and y - intercept is 6, where a, b, and c are integers with no factor common to all three, and a≥0. what is the slope of the line whose x - intercept is 18 and y - intercept is 6? a. the slope is (type an integer or a simplified fraction.) b. the slope is undefined. the equation of the line is (simplify your answer.)

Explanation:

Step1: Identify the intercept points

The x - intercept is 18, so the point on the line is (18,0). The y - intercept is 6, so the point on the line is (0,6).

Step2: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(18,0)$ and $(x_2,y_2)=(0,6)$. So $m=\frac{6 - 0}{0 - 18}=-\frac{1}{3}$.

Step3: Use the slope - intercept form to find the equation

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $m =-\frac{1}{3}$ and $b = 6$, so $y=-\frac{1}{3}x+6$.

Step4: Convert to the general form

Multiply through by 3 to get $3y=-x + 18$. Then, rearrange to $x+3y = 18$.

Answer:

A. The slope is $-\frac{1}{3}$
The equation of the line is $x + 3y=18$