Question

write an equation of the line in slope - intercept form given the slope and y - intercept

1. slope: $-\frac{1}{3}$, y - intercept: 5
2. slope: 4, y - intercept: -7

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is given by the formula \(y=mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\) - intercept.

Step2: Solve for the first equation

For the first problem, we are given that the slope \(m =-\frac{1}{3}\) and the \(y\) - intercept \(b = 5\).
Substitute \(m=-\frac{1}{3}\) and \(b = 5\) into the slope - intercept form \(y=mx + b\).
We get \(y=-\frac{1}{3}x+5\).

Step3: Solve for the second equation

For the second problem, we are given that the slope \(m = 4\) and the \(y\) - intercept \(b=-7\).
Substitute \(m = 4\) and \(b=-7\) into the slope - intercept form \(y=mx + b\).
We get \(y = 4x-7\).

Answer:

1. \(y=-\frac{1}{3}x + 5\)
2. \(y = 4x-7\)