Question

4 graph each linear equation on the grid provided. be sure to label the units on the x- and y-axes.
y = -2x + 1

y = -\frac{3}{4}x + 2

5x + 2y = 10

Explanation:

For \( y = -2x + 1 \)

Step1: Identify slope and y-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( m=-2 \) (slope) and \( b = 1 \) (y - intercept).

Step2: Plot the y - intercept

Plot the point \( (0,1) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m=-2=\frac{-2}{1} \). From the point \( (0,1) \), move down 2 units and right 1 unit to get the point \( (1, - 1) \).

Step4: Draw the line

Draw a straight line through the points \( (0,1) \) and \( (1,-1) \). Label the x - axis and y - axis with a scale (e.g., each grid square represents 1 unit).

For \( y=-\frac{3}{4}x + 2 \)

Step1: Identify slope and y - intercept

In the slope - intercept form \( y = mx + b \), \( m=-\frac{3}{4} \) (slope) and \( b = 2 \) (y - intercept).

Step2: Plot the y - intercept

Plot the point \( (0,2) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m =-\frac{3}{4}\). From the point \( (0,2) \), move down 3 units and right 4 units to get the point \( (4,-1) \).

Step4: Draw the line

Draw a straight line through the points \( (0,2) \) and \( (4,-1) \). Label the x - axis and y - axis with a scale (e.g., each grid square represents 1 unit).

For \( 5x+2y = 10 \)

Step1: Rewrite in slope - intercept form

Solve for \( y \):
\[

$$\begin{align*} 2y&=-5x + 10\\ y&=-\frac{5}{2}x+5 \end{align*}$$

\]
Here, \( m =-\frac{5}{2} \) (slope) and \( b = 5 \) (y - intercept).

Step2: Plot the y - intercept

Plot the point \( (0,5) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m=-\frac{5}{2}=\frac{-5}{2} \). From the point \( (0,5) \), move down 5 units and right 2 units to get the point \( (2,0) \).

Step4: Draw the line

Draw a straight line through the points \( (0,5) \) and \( (2,0) \). Label the x - axis and y - axis with a scale (e.g., each grid square represents 1 unit).

(Note: Since the problem is about graphing linear equations, the final "answer" is the graphical representation as described above. If we were to describe the key points for each line:

For \( y=-2x + 1 \): passes through \( (0,1) \) and \( (1,-1) \)

For \( y =-\frac{3}{4}x+2 \): passes through \( (0,2) \) and \( (4,-1) \)

For \( 5x + 2y=10 \) (or \( y=-\frac{5}{2}x + 5 \)): passes through \( (0,5) \) and \( (2,0) \))

Answer:

For \( y=-2x + 1 \): Line through \( (0,1) \) and \( (1,-1) \) (x - y axes labeled with 1 - unit grid).
For \( y =-\frac{3}{4}x+2 \): Line through \( (0,2) \) and \( (4,-1) \) (x - y axes labeled with 1 - unit grid).
For \( 5x + 2y = 10 \): Line through \( (0,5) \) and \( (2,0) \) (x - y axes labeled with 1 - unit grid).