What is the equation of the line in slope-intercept form?

Question

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So on this graph on the x line we have -5 to 1 on the left and on the right we have 1 to 5. Okay now on y the line that is up is 6 to 1 and the y that is down in -1 to -4

The line is going to the left at an angle across the line is on (-3,0) and (0,4)

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).

1. Find the slope (m): The slope is calculated using the formula:

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Using the points (-3, 0) and (0, 4):

   Let \((x_1, y_1) = (-3, 0)\) and \((x_2, y_2) = (0, 4)\).

   \[ m = \frac{4 - 0}{0 - (-3)} = \frac{4}{3} \]

2. Find the y-intercept (b): The y-intercept is the value of y when x = 0. From the second point (0, 4), we can see that the y-intercept \(b = 4\).

3. Write the equation in slope-intercept form: Now that we have the slope and y-intercept, we can write the equation of the line:

   \[ y = \frac{4}{3}x + 4 \]

So, the equation of the line in slope-intercept form is:

\[ y = \frac{4}{3}x + 4 \]