Let's break down the tasks in the image you've provided.

Ch. 3: 104

Find the coordinates of the points of intersection of the graphs with the coordinate axes for the following equations:

a. $y = -1.5x + 3$

To find the intersection with the axes, we need the points where the graph crosses the $x$-axis and the $y$-axis:

• Intersection with the $y$-axis: Set $x = 0$. $y = -1.5(0) + 3 = 3$ So, the intersection with the $y$-axis is at $(0, 3)$.

• Intersection with the $x$-axis: Set $y = 0$. $0 = -1.5x + 3$ $1.5x = 3 \quad \Rightarrow \quad x = 2$ So, the intersection with the $x$-axis is at $(2, 0)$.

e. $y = 0.8x - 0.6$

• Intersection with the $y$-axis: Set $x = 0$. $y = 0.8(0) - 0.6 = -0.6$ So, the intersection with the $y$-axis is at $(0, -0.6)$.

• Intersection with the $x$-axis: Set $y = 0$. $0 = 0.8x - 0.6$ $0.8x = 0.6 \quad \Rightarrow \quad x = \frac{0.6}{0.8} = 0.75$ So, the intersection with the $x$-axis is at $(0.75, 0)$.

Ch. 3: 103

Find the $x$- and $y$-intercepts for the following equations:

f. $3x - 2y = 0$

• Intersection with the $y$-axis: Set $x = 0$. $3(0) - 2y = 0 \quad \Rightarrow \quad -2y = 0 \quad \Rightarrow \quad y = 0$ So, the intersection with the $y$-axis is $(0, 0)$.

• Intersection with the $x$-axis: Set $y = 0$. $3x - 2(0) = 0 \quad \Rightarrow \quad 3x = 0 \quad \Rightarrow \quad x = 0$ So, the intersection with the $x$-axis is $(0, 0)$.

g. $2x + 5y - 11 = 0$

• Intersection with the $y$-axis: Set $x = 0$. $2(0) + 5y - 11 = 0 \quad \Rightarrow \quad 5y = 11 \quad \Rightarrow \quad y = \frac{11}{5} = 2.2$ So, the intersection with the $y$-axis is $(0, 2.2)$.

• Intersection with the $x$-axis: Set $y = 0$. $2x + 5(0) - 11 = 0 \quad \Rightarrow \quad 2x = 11 \quad \Rightarrow \quad x = \frac{11}{2} = 5.5$ So, the intersection with the $x$-axis is $(5.5, 0)$.

Ch. 3: 107

Construct graphs for the equations:

c. $y = \frac{1}{4}$

This is a horizontal line where the value of $y$ is always $\frac{1}{4}$. The line intersects the $y$-axis at $(0, \frac{1}{4})$ and runs parallel to the $x$-axis.

3044: Graph all points that satisfy the given equation.

c. $x = 2$

This is a vertical line where the value of $x$ is always 2. The line intersects the $x$-axis at $(2, 0)$ and runs parallel to the $y$-axis.

Would you like to go over any of these steps in more detail, or do you have any other questions? Here's some related exploration:

1. How would you graph a linear equation when you know the intercepts?
2. What happens if the slope is zero or undefined in an equation?
3. Can you solve systems of equations using intercepts?
4. How does the slope of a line affect its intersections with the axes?
5. What if the graph of the equation is not a straight line?

Tip: Always start by finding the intercepts (where the graph crosses the axes) to quickly sketch the graph of a line!