Problem 42
Question
Describe how to write the equation of a line if two points on the line are known.
Step-by-Step Solution
Verified Answer
To write the equation of a line with two known points, calculate the slope using the formula \(\frac{(y_2 - y_1)}{(x_2 - x_1)}\), substitute the slope and one of the points into the equation \(y = mx + c\), solve for \(c\), then write the final equation by substituting \(m\) and \(c\) with their calculated values.
1Step 1: Calculate the slope of the line
Given two points \(A(x_1, y_1)\) and \(B(x_2, y_2)\) on a line, we can calculate the slope of the line (\(m\)) using the formula: \[m = \frac{(y_2 - y_1)}{(x_2 - x_1)}\]
2Step 2: Substitute one point and the slope into the slope-intercept form
The slope-intercept form of a line's equation is \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. Substitute the calculated slope and one of the points (say, \(A(x_1, y_1)\)) into this equation, giving \[y_1 = m x_1 + c\] Then, solve this equation for \(c\) to get the y-intercept.
3Step 3: Write the equation of the line
The final equation of the line will be in the form \(y = mx + c\), by substituting \(m\) and \(c\) with their calculated values.
Other exercises in this chapter
Problem 42
Write each sentence as a linear inequality in two variables. Then graph the inequality. The \(y\) -variable is no less than \(\frac{1}{4}\) of the \(x\) -variab
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determine whether each ordered pair is a solution of the given equation. $$y=8-4 x \quad(8,0),(16,-2),(3,-4)$$
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a.) Put the equation in slope-intercept form by solving for \(y .\) b.) Identify the slope and the \(y\) -intercept. c.) Use the slope and y-intercept to graph
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The line passing through \((1, y)\) and \((7,12)\) is parallel to the line joining \((-3,4)\) and \((-5,-2) .\) Find \(y\)
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