Question

question
what is the equation of the line that passes through the point (6, 0) and has a slope of $-\frac{5}{6}$?
answer
attempt 1 out of 2

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 6$, $y_1=0$ and $m=-\frac{5}{6}$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 6$, $y_1 = 0$ and $m=-\frac{5}{6}$ into the point - slope formula:
$y-0=-\frac{5}{6}(x - 6)$

Step3: Simplify the equation

Simplify the left - hand side: $y=-\frac{5}{6}(x - 6)$
Distribute the $-\frac{5}{6}$ on the right - hand side: $y=-\frac{5}{6}x+(-\frac{5}{6})\times(- 6)$
Calculate $(-\frac{5}{6})\times(-6)=5$. So the equation becomes $y =-\frac{5}{6}x + 5$. We can also write it in standard form $Ax+By = C$. Multiply through by 6 to get $6y=-5x + 30$, and then $5x+6y=30$. But the slope - intercept form $y=-\frac{5}{6}x + 5$ is also a correct form.

Answer:

The equation of the line is $y=-\frac{5}{6}x + 5$ (or $5x + 6y=30$)