Question

practice & problem solving

1. leveled practice what is the graph of the equation ( y = 2x + 4 )?

the ( y )-intercept is (square), which means the line crosses the ( y )-axis at
point ((square), (square)). plot this point.
the slope of the line is positive, so it goes from left to righ
start at the ( y )-intercept. move up (square), and then move right
you are now at the point ((square), (square)). plot this point.
draw a line to connect the two points.

1. write an equation for the line in slope - intercept form.
2. v

Explanation:

Step1: Find the y - intercept

The equation of a line in slope - intercept form is \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=2x + 4\), comparing with \(y=mx + b\), we have \(b = 4\). So the y - intercept is 4. When \(x = 0\) (since on the y - axis, the x - coordinate is 0), \(y=2(0)+4=4\). So the line crosses the y - axis at the point \((0,4)\).

Step2: Analyze the slope

The slope \(m\) of the line \(y = 2x+4\) is 2. The slope \(m=\frac{\text{rise}}{\text{run}}\), so a slope of 2 means \(\frac{\text{rise}}{\text{run}}=\frac{2}{1}\), which means we move up 2 units and then move right 1 unit from the y - intercept \((0,4)\).

Step3: Find the new point

Starting from \((0,4)\), moving up 2 units (the y - coordinate increases by 2: \(4 + 2=6\)) and moving right 1 unit (the x - coordinate increases by 1: \(0+1 = 1\)). So the new point is \((1,6)\).

Answer:

s (filling in the blanks):
The y - intercept is \(\boldsymbol{4}\), which means the line crosses the y - axis at the point \((\boldsymbol{0},\boldsymbol{4})\).

The slope of the line is positive, so it goes \(\boldsymbol{up}\) from left to right.

Start at the y - intercept. Move up \(\boldsymbol{2}\), and then move right \(\boldsymbol{1}\).

You are now at the point \((\boldsymbol{1},\boldsymbol{6})\).