To find the equations of the lines in the form \(y = mx + b\) (slope-intercept form) for lines J, K, and L, we need to determine the slope (\(m\)) and the y-intercept (\(b\)) for each line based on the given points.
Line J
Given points: \(A(0, 8)\) and \(B(3, 0)\)
First, we will calculate the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the points: \[ m = \frac{0 - 8}{3 - 0} = \frac{-8}{3} \]
Now, using the y-intercept where the line crosses the y-axis at point A (0, 8), we can write the equation: \[ y = -\frac{8}{3}x + 8 \]
Line K
Given points: \(E(5, -5)\) and \(F(0, -3)\)
Calculating the slope \(m\) using the same formula: \[ m = \frac{-3 - (-5)}{0 - 5} = \frac{-3 + 5}{0 - 5} = \frac{2}{-5} = -\frac{2}{5} \]
Using point F (0, -3) as the y-intercept: \[ y = -\frac{2}{5}x - 3 \]
Line L
Given points: \(C(-7, 0)\) and \(D(0, 3)\)
Calculating the slope \(m\): \[ m = \frac{3 - 0}{0 - (-7)} = \frac{3}{7} \]
Using point D (0, 3) as the y-intercept: \[ y = \frac{3}{7}x + 3 \]
Summary of the equations
- Line J: \(y = -\frac{8}{3}x + 8\)
- Line K: \(y = -\frac{2}{5}x - 3\)
- Line L: \(y = \frac{3}{7}x + 3\)