Question

How to write an equation in intercept slope line When the line passes through the y axis at 40 and x axis is 15

Answer 1

To write the equation of a line in slope-intercept form (which is \( y = mx + b \)), you need the slope \( m \) and the y-intercept \( b \).

From the information you've provided:
- The line passes through the y-axis at 40, which means the y-intercept \( b = 40 \).
- The line passes through the x-axis at 15, which means the x-intercept is 15. The x-intercept is the point where \( y = 0 \), so we can use the x-intercept to find another point on the line: \( (15, 0) \).

Now we have two points:
1. The y-intercept: \( (0, 40) \)
2. The x-intercept: \( (15, 0) \)

Next, we can calculate the slope \( m \) using the formula for the slope between two points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 40) \) and \( (15, 0) \):
\[
m = \frac{0 - 40}{15 - 0} = \frac{-40}{15} = -\frac{8}{3}
\]

Now we have \( m = -\frac{8}{3} \) and \( b = 40 \).

Therefore, the equation of the line in slope-intercept form is:
\[
y = -\frac{8}{3}x + 40
\]