1. For the equation \( y = \frac{3}{4}x + 2 \), the slope \( m = \frac{3}{4} \) and the y-intercept \( b = 2 \). This is derived from the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The line passes through the point (0, 2) and rises 3 units for every 4 units it moves to the right.
2. For the equation \( y = \frac{2}{3}x + 7 \), the slope \( m = \frac{2}{3} \) and the y-intercept \( b = 7 \). This means the line crosses the y-axis at (0, 7) and rises 2 units for every 3 units it moves to the right.
3. For the equation \( y = -\frac{3}{2}x + 4 \), the slope \( m = -\frac{3}{2} \) and the y-intercept \( b = 4 \). The line crosses the y-axis at (0, 4) and falls 3 units for every 2 units it moves to the right.
4. For the equation \( y = \frac{2}{3}x + 7 \), the slope \( m = \frac{2}{3} \) and the y-intercept \( b = 7 \). The line passes through (0, 7) and rises 2 units for every 3 units it moves to the right.
5. The graph of \( y = \frac{1}{2}x + 1 \) has a slope of \( \frac{1}{2} \) and a y-intercept at (0, 1). Starting from (0, 1), the line rises 1 unit for every 2 units it moves to the right.
6. The graph of \( y = x - 1 \) has a slope of 1 and a y-intercept at (0, -1). Starting from (0, -1), the line rises 1 unit for every 1 unit it moves to the right.
7. The graph of \( y = -x + 2 \) has a slope of -1 and a y-intercept at (0, 2). Starting from (0, 2), the line falls 1 unit for every 1 unit it moves to the right.
8. The graph of \( y = 4 \) is a horizontal line passing through all points where \( y = 4 \). It has a slope of 0 and a y-intercept at (0, 4).
9. The graph of \( x = 2 \) is a vertical line passing through all points where \( x = 2 \). It has an undefined slope and no y-intercept.
10. The graph of \( y = -\frac{1}{4}x \) has a slope of \( -\frac{1}{4} \) and a y-intercept at (0, 0). Starting from (0, 0), the line falls 1 unit for every 4 units it moves to the right.
Parent Tip: Review the logic above to help your child master the concept of slope intercept form worksheet 8th grade.
