Question

What linear equation in slope intercept from does this graph represent?​

Answer 1

Answer:

$y = 16\frac{2}{3} x + 100$ or $y = \frac{50}{3} + 100$

Step-by-step explanation:

The equation of a line is $y = mx + b$, with $m$ being the slope and $b$ being the y-intercept.

We can see on the graph that the y-intercept, where the line crosses or touches the y-axis, is 100. So, our new equation is $y = mx + 100$.

Now we have to find the slope. Let's pick a point that's clearly on the graph. Perhaps (3, 150). And then we'll take the y-intercept point for convenience, (0, 100).

Then, we'll use $\frac{y_{2} - y_{1}}{x_{2} - x_{1} }$ to find the slope.

Let's substitute in our points.

$\frac{150-100}{3-0}$

Simplify.

$\frac{50}{3}$

Now, we can leave the slope like that or turn it into a mixed number. As a mixed number, your slope is $16\frac{2}{3}$.

We'll put that in our equation for a line and...bam!

$y = 16\frac{2}{3} x + 100$ or $y = \frac{50}{3} + 100$