Question

which equation represents the graph of a line on a coordinate plane that passes through the x-intercept at (9,0) and the y-intercept at (0,−5) ?
a $y = -\frac{9}{5}x - 5$
b $y = \frac{9}{5}x - 5$
c $y = -\frac{5}{9}x - 5$
d $y = \frac{5}{9}x - 5$

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We know the \(y\) - intercept \(b=- 5\) (since the line passes through \((0,-5)\)).

Step2: Calculate the slope \(m\)

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We have the points \((9,0)\) (where \(x_1 = 9,y_1 = 0\)) and \((0,-5)\) (where \(x_2=0,y_2=-5\)).
Substitute the values into the slope formula: \(m=\frac{-5 - 0}{0 - 9}=\frac{-5}{-9}=\frac{5}{9}\).

Step3: Write the equation of the line

Using the slope - intercept form \(y=mx + b\) with \(m = \frac{5}{9}\) and \(b=-5\), the equation of the line is \(y=\frac{5}{9}x-5\).

Answer:

D. \(y=\frac{5}{9}x - 5\)