Question

Consider the graph below: What is the equation of the line in slope-intercept form?

Answer 1

Answer:

$y=\frac{-5}{4}x+5$

Step-by-step explanation:

Slope intercept form: $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept (the value of y when the line crosses the y-axis)

1) Find the slope of the line ($m$)

To do this, we can plug the two given points (0,5) and (4,0) into the slope equation:

$\frac{y_2-y_1}{x_2-x_1} \\= \frac{0-5}{4-0}\\= \frac{-5}{4}$

Therefore, the slope of the line is $\frac{-5}{4}$.

2) Find the y-intercept of the line ($b$)

Recall that the y-intercept is the value of y when the line crosses the y-axis. We don't actually need to perform any calculations because on the graph, we can see that the line crosses the y-axis when y=5.

Therefore, the y-intercept of the line is 5.

Plugging both $m$ and $b$ into $y=mx+b$, we have a final equation of:

$y=\frac{-5}{4}x+5$

I hope this helps!