Question

Write the slope-intercept form of the equation of each line?

Answer 1

Problem 1

It appears the line is going through the points (-1,-4) and (0,5)

Let's find the slope

$(x_1,y_1) = (-1,-4) \text{ and } (x_2,y_2) = (0,5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{5 - (-4)}{0 - (-1)}\\\\m = \frac{5 + 4}{0 + 1}\\\\m = \frac{9}{1}\\\\m = 9$

The slope is 9

The y intercept is b = 5 as this is where the graph crosses the y axis.

We go from y = mx+b to y = 9x+5

Answer:   y = 9x+5

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Problem 2

This line goes through the points (0,4) and (5,5)

We'll follow the same exact steps as before

First we need the slope

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (5,5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{5 - 4}{5 - 0}\\\\m = \frac{1}{5}$

The y intercept is the y coordinate of (0,4) so it's b = 4

Answer:  $y = \frac{1}{5}x+4$