Question

graphing a linear equation of the form y = mx + b continued
⑤ y = (10/3)x - 5
⑥ y = - (3/4)x + 2

Explanation:

Step1: Identify the slope and y-intercept

For the equation \( y = \frac{10}{3}x - 5 \), the slope \( m=\frac{10}{3} \) and the y-intercept \( b = -5 \). For \( y = -\frac{3}{4}x + 2 \), the slope \( m = -\frac{3}{4} \) and the y-intercept \( b = 2 \).

Step2: Plot the y-intercept

For \( y=\frac{10}{3}x - 5 \), plot the point \( (0, -5) \). For \( y = -\frac{3}{4}x + 2 \), plot the point \( (0, 2) \).

Step3: Use the slope to find another point

For \( y=\frac{10}{3}x - 5 \), from \( (0, -5) \), move up 10 units and right 3 units (since slope is \( \frac{10}{3} \)) to get \( (3, 5) \). For \( y = -\frac{3}{4}x + 2 \), from \( (0, 2) \), move down 3 units and right 4 units (since slope is \( -\frac{3}{4} \)) to get \( (4, -1) \).

Step4: Draw the line

Connect the two points for each equation to draw the line.

Answer:

To graph \( y=\frac{10}{3}x - 5 \): Plot \( (0, -5) \) and \( (3, 5) \), then draw a line through them. To graph \( y = -\frac{3}{4}x + 2 \): Plot \( (0, 2) \) and \( (4, -1) \), then draw a line through them.