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Finding the Equation of a Line

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Questions and Answers

What is the slope of the line that passes through the points (0, 5) and (2, 8)?

1.5 (correct)

What is the y-intercept of the line represented by the equation y = 1.5x + 5?

5 (correct)

1.5

2.5

Which formula is used to calculate the slope of a line?

m = (y₂ - y₁) / (x₂ - x₁) (correct)

m = (y₁ - y₂) / (x₁ - x₂)

y = mx + b

m = (x₂ - x₁) / (y₂ - y₁)

What would the equation of the line be if the slope were 3 and the y-intercept remained 5?

<p>y = 3x + 5</p> Signup and view all the answers

If a line has a slope of 1.5, what can be inferred about the relationship between x and y?

<p>For every 1 unit increase in x, y increases by 1.5 units.</p> Signup and view all the answers

Study Notes

Finding the Equation of a Line

The equation of a straight line is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
The slope (m) of a line is calculated as the change in y divided by the change in x between two points on the line.
The y-intercept (b) is the point where the line crosses the y-axis.
In the given example, the line passes through the points (0, 5) and (2, 8).
Using the formula for slope, m = (8 - 5) / (2 - 0) = 1.5.
The y-intercept is 5, as observed from the graph.
Therefore, the equation of the line is y = 1.5x + 5.

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Description

This quiz focuses on determining the equation of a straight line using the slope-intercept form. You will explore how to calculate the slope and y-intercept based on given points and apply these concepts to find the line's equation. Test your understanding of these fundamental algebraic principles.