Questions: Match each linear equation with its graph Equation Graph Color y=5x-3 a. blue (B) y=-3x-2 b. purple (P) y=-5x-3 c. green (G) y=-4 d. black (K) y=1/4x-2 e. red (R)

Transcript text: Match each linear equation with its graph Equation Graph Color $y=5 x-3$ a. blue (B) $y=-3 x-2$ b. purple (P) $y=-5 x-3$ c. green $(\mathrm{G})$ $y=-4$ d. black (K) $y=\frac{1}{4} x-2$ e. red (R)

Solution

Solution Steps

Step 1: Identify the y-intercepts

Equation 1: $ y = 5x - 3 $ has a y-intercept of -3.
Equation 2: $ y = -3x - 2 $ has a y-intercept of -2.
Equation 3: $ y = -5x - 3 $ has a y-intercept of -3.
Equation 4: $ y = -4 $ is a horizontal line with a y-intercept of -4.
Equation 5: $ y = \frac{1}{4}x - 2 $ has a y-intercept of -2.

Step 2: Match y-intercepts with graphs

The purple line (P) intersects the y-axis at -4, so it corresponds to $ y = -4 $.
The red line (R) intersects the y-axis at -2, so it corresponds to either $ y = -3x - 2 $ or $ y = \frac{1}{4}x - 2 $.
The blue (B) and green (G) lines intersect the y-axis at -3, so they correspond to either $ y = 5x - 3 $ or $ y = -5x - 3 $.

Step 3: Determine the slopes

The red line (R) has a positive slope, so it corresponds to $ y = \frac{1}{4}x - 2 $.
The black line (K) has a negative slope and intersects the y-axis at -2, so it corresponds to $ y = -3x - 2 $.
The blue line (B) has a positive slope, so it corresponds to $ y = 5x - 3 $.
The green line (G) has a negative slope, so it corresponds to $ y = -5x - 3 $.