Question

graph the linear equation, then use the graph to identify the x-intercept.

1. $y = \frac{2}{3}x - 4$
2. $y = -5x + 10$

for 10: m=\frac{2}{3} b=-4
x-intercept =
for 11: m=-5 b=10
x-intercept =

Explanation:

Problem 10: \( y = \frac{2}{3}x - 4 \)

Step 1: Recall the slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For \( y = \frac{2}{3}x - 4 \), we can identify:
\( m = \frac{2}{3} \), \( b = -4 \)

Step 2: Find the x-intercept

The x-intercept is the value of \( x \) when \( y = 0 \). Set \( y = 0 \) in the equation:
\( 0 = \frac{2}{3}x - 4 \)

Step 3: Solve for \( x \)

Add 4 to both sides:
\( 4 = \frac{2}{3}x \)

Multiply both sides by \( \frac{3}{2} \):
\( x = 4 \times \frac{3}{2} = 6 \)

Step 1: Recall the slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For \( y = -5x + 10 \), we can identify:
\( m = -5 \), \( b = 10 \)

Step 2: Find the x-intercept

The x-intercept is the value of \( x \) when \( y = 0 \). Set \( y = 0 \) in the equation:
\( 0 = -5x + 10 \)

Step 3: Solve for \( x \)

Subtract 10 from both sides:
\( -10 = -5x \)

Divide both sides by \( -5 \):
\( x = \frac{-10}{-5} = 2 \)

Answer:

\( m = \boldsymbol{\frac{2}{3}} \), \( b = \boldsymbol{-4} \), \( x \)-intercept \( = \boldsymbol{6} \)

Problem 11: \( y = -5x + 10 \)