Linear Functions, Slope, and Rate of Change – Precalculus Study Guidance

Q22. Find the equation of the line with slope $\frac{1}{3}$ passing through the origin.

Background

Topic: Linear Equations

This question tests your ability to write the equation of a line given its slope and a point it passes through (the origin).

Key Terms and Formulas

• Slope-intercept form: $y = mx + b$

• Point-slope form: $y - y_1 = m(x - x_1)$

• Origin: $(0, 0)$

Step-by-Step Guidance

1. Identify the slope $m = \frac{1}{3}$ and the point $(0, 0)$.

2. Use the point-slope form: $y - y_1 = m(x - x_1)$, substituting the values.

3. Simplify the equation to slope-intercept form $y = mx + b$.

Try solving on your own before revealing the answer!

Q23. Find the equation of the line with slope $-\frac{2}{3}$ passing through $(6, -2)$.

Background

Topic: Linear Equations

This question tests your ability to write the equation of a line given its slope and a specific point.

Key Terms and Formulas

• Slope-intercept form: $y = mx + b$

• Point-slope form: $y - y_1 = m(x - x_1)$

Step-by-Step Guidance

1. Identify the slope $m = -\frac{2}{3}$ and the point $(6, -2)$.

2. Plug these values into the point-slope form: $y - (-2) = -\frac{2}{3}(x - 6)$.

3. Simplify the equation to slope-intercept form $y = mx + b$.

Try solving on your own before revealing the answer!

Q24. Find the equation of the line with slope $-\frac{3}{5}$ passing through $(10, -4)$.

Background

Topic: Linear Equations

This question tests your ability to write the equation of a line given its slope and a specific point.

Key Terms and Formulas

• Slope-intercept form: $y = mx + b$

• Point-slope form: $y - y_1 = m(x - x_1)$

Step-by-Step Guidance

1. Identify the slope $m = -\frac{3}{5}$ and the point $(10, -4)$.

2. Plug these values into the point-slope form: $y - (-4) = -\frac{3}{5}(x - 10)$.

3. Simplify the equation to slope-intercept form $y = mx + b$.

Try solving on your own before revealing the answer!

Q25. Find the equation of the line passing through $(1, 2)$ and $(5, 10)$.

Background

Topic: Linear Equations

This question tests your ability to find the equation of a line given two points.

Key Terms and Formulas

• Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Point-slope form: $y - y_1 = m(x - x_1)$

Step-by-Step Guidance

1. Calculate the slope $m$ using the two points: $(1, 2)$ and $(5, 10)$.

2. Choose one of the points and use the point-slope form to write the equation.

3. Simplify to slope-intercept form $y = mx + b$.

Try solving on your own before revealing the answer!

Q26. Find the equation of the line passing through $(3, 5)$ and $(8, 15)$.

Background

Topic: Linear Equations

This question tests your ability to find the equation of a line given two points.

Key Terms and Formulas

• Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Point-slope form: $y - y_1 = m(x - x_1)$

Step-by-Step Guidance

1. Calculate the slope $m$ using the two points: $(3, 5)$ and $(8, 15)$.

2. Choose one of the points and use the point-slope form to write the equation.

3. Simplify to slope-intercept form $y = mx + b$.

Try solving on your own before revealing the answer!

Q27. Find the equation of the line passing through $(-3, 0)$ and $(0, 3)$.

Background

Topic: Linear Equations

This question tests your ability to find the equation of a line given two points.

Key Terms and Formulas

• Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Point-slope form: $y - y_1 = m(x - x_1)$

Step-by-Step Guidance

1. Calculate the slope $m$ using the two points: $(-3, 0)$ and $(0, 3)$.

2. Choose one of the points and use the point-slope form to write the equation.

3. Simplify to slope-intercept form $y = mx + b$.

Try solving on your own before revealing the answer!