Question

In Exercise 4.5, we give linear equations. For each equation,

a. find the $y$-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Given equation is,

$y=4x+3$

Short answer

a. $y$-intercept is $3$and slope is $4$

b. Slope is upward for given linear equation.

c. The graph is given below.

Step-by-step solution

Part(a) Step 1: Given information

We need to find $y$-intercept and slope of given linear equation.

Part(a) Step 2: Calculations

General form of linear equation is $y=mx+c$where $m$is slope and $c$is intercept.

Comparing $y=4x+3$with general form we get,

slope $m=4$

y-intercept$c=3$.

Part(b) Step 1: Given information

We have to determine the direction of slope of given linear equation.

Part(b) Step 2: Answer and its explanation

As we see the slope is having positive sign so the slope will point in upward direction.

Part(c) Step 1: Given information

We have to graph the equation.

Part(c) Step 2: Explanation

The graph is given below