Q13. Rewrite in slope-intercept form. Then state the zero (x-intercept) of the function.

Background

Topic: Linear Equations – Slope-Intercept Form and Intercepts

This question tests your ability to manipulate a linear equation into slope-intercept form () and to find the x-intercept (also called the zero) of the function.

Key Terms and Formulas:

• Slope-intercept form: , where is the slope and is the y-intercept.

• x-intercept (zero): The value of when .

Step-by-Step Guidance

1. Start with the given equation: .

2. Rearrange the equation to solve for in terms of (get $y$ by itself on one side).

3. Once in form, identify the slope and y-intercept.

4. To find the x-intercept, set in your equation and solve for .

Try solving on your own before revealing the answer!

Q15. Which equation represents a line with slope and y-intercept $2$?

Background

Topic: Linear Equations – Identifying Slope and Intercept

This question tests your ability to recognize the equation of a line in slope-intercept form () given a specific slope and y-intercept.

Key Terms and Formulas:

• Slope-intercept form:

• Slope (): The coefficient of

• y-intercept (): The constant term

Step-by-Step Guidance

1. Recall that the equation of a line with slope and y-intercept is .

2. Plug in and into the formula.

3. Compare your result to the answer choices to find the matching equation.

Try solving on your own before revealing the answer!

Q16. Which equation is parallel to and passes through ?

Background

Topic: Parallel Lines and Point-Slope Form

This question tests your understanding of parallel lines (same slope) and writing the equation of a line through a given point.

Key Terms and Formulas:

• Slope of a line: For , slope is

• Parallel lines: Have the same slope

• Point-slope form:

Step-by-Step Guidance

1. Find the slope of by rewriting in slope-intercept form or using .

2. Since parallel lines have the same slope, use this slope for your new line.

3. Use the point-slope form with the point and the slope you found.

4. Simplify to slope-intercept form () and compare to the answer choices.

Try solving on your own before revealing the answer!

Q17. Write the equation of the line that passes through and has slope $2$ in point-slope form and slope-intercept form.

Background

Topic: Writing Equations of Lines

This question tests your ability to use point-slope and slope-intercept forms to write the equation of a line given a point and a slope.

Key Terms and Formulas:

• Point-slope form:

• Slope-intercept form:

Step-by-Step Guidance

1. Use the point-slope form with , , .

2. Write the equation in point-slope form: .

3. Expand and simplify to get the equation in slope-intercept form ().

Try solving on your own before revealing the answer!

Q18. The equation is given. Find its slope, x-intercept, and y-intercept.

Background

Topic: Linear Equations – Slope and Intercepts

This question tests your ability to find the slope, x-intercept, and y-intercept of a line given in standard form.

Key Terms and Formulas:

• Standard form:

• Slope:

• x-intercept: Set and solve for

• y-intercept: Set and solve for

Step-by-Step Guidance

1. Identify , , in the equation .

2. Find the slope using .

3. To find the x-intercept, set and solve for .

4. To find the y-intercept, set and solve for .

Try solving on your own before revealing the answer!