Questions: Match each linear equation with its graph Equation a) y = 3x b) y = 1 - x c) y = 4x + 4 d) y = 3x - 1 e) y = 3 Graph Color a) blue b) black c) red d) purple e) green a) y = 3x b) y = 1 - x c) y = 4x + 4 d) y = 3x - 1 e) y = 3

Match each linear equation with its graph

Equation
a) y = 3x
b) y = 1 - x
c) y = 4x + 4
d) y = 3x - 1
e) y = 3

Graph Color
a) blue
b) black
c) red
d) purple
e) green

a) y = 3x
b) y = 1 - x
c) y = 4x + 4
d) y = 3x - 1
e) y = 3

Transcript text: Match each linear equation with its graph Equation a) y = 3x b) y = 1 - x c) y = 4x + 4 d) y = 3x - 1 e) y = 3 Graph Color a) blue b) black c) red d) purple e) green $\begin{array}{l} a) y = 3x \\ b) y = 1 - x \\ c) y = 4x + 4 \\ d) y = 3x - 1 \\ e) y = 3 \end{array}$

Solution

Solution Steps

Step 1: Analyze the equations and the graph

We are given five linear equations and a graph with five lines of different colors. We need to match each equation with its corresponding graph. We can do this by analyzing the slopes and y-intercepts of the equations.

Step 2: Match the equations to the lines

y = 3x - 1 (Blue): This equation has a slope of 3 and a y-intercept of -1. The blue line has a positive slope and crosses the y-axis below the origin, which matches the equation.
y = (1/4)x + 4 (Black): This equation has a slope of 1/4 and a y-intercept of 4. The black line has a positive, less steep slope than the blue line, and it crosses the y-axis above the origin, consistent with the equation.
y = -x/4 + 4 (Red): This equation has a slope of -1/4 and a y-intercept of 4. The red line has a negative slope and crosses the y-axis above the origin.
y = -3x - 1 (Purple): This equation has a slope of -3 and a y-intercept of -1. The purple line has a negative, steep slope and crosses the y-axis below the origin.
y = -x + 4 (Green): This equation has a slope of -1 and a y-intercept of 4. The green line has a negative slope and crosses the y-axis above the origin. It is steeper than the red line, corresponding to a slope with a larger magnitude.
y = 3 (Horizontal Line): This line is horizontal and corresponds to a constant y-value of 3.