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Chapter 2: Problem 94

Describe how to write the equation of a line if the coordinates of two points along the line are known.

Short Answer

Expert verified
The equation of the line is obtained by first calculating the slope using the formula (y2 - y1) / (x2 - x1), then substituting the slope and one of the coordinates into the equation y = mx + b to find the y-intercept, and finally substituting these into the same equation to get the line's equation.

Step by step solution

01

Calculate Slope

First, determine the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the known points. The slope is the ratio of the vertical change (y2 - y1) to the horizontal change (x2 - x1).
02

Calculate y-Intercept

Next, substitute the slope and the coordinates of one of the points into the equation y = mx + b. Here, 'm' is the slope, 'b' is the y-intercept, and (x, y) are the coordinates of the point. Solving this equation for 'b' gives the y-intercept.
03

Formulate the Equation of the Line

Finally, substitute the calculated slope ('m') and y-intercept ('b') into the equation y = mx + b. This equation represents the line passing through the given points.

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Most popular questions from this chapter

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned} (x-2)^{2}+(y+3)^{2} &=4 \\ y &=x-3 \end{aligned}$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-10 x-6 y-30=0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In graph of \((x-2)^{2}+(y+1)^{2}=16\) is my graph of \(x^{2}+y^{2}=16\) translated two units right and one unit down.

Solve each quadratic equation by the method of your choice. $$-x^{2}-2 x+1=0$$

Explaining the Concepts Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?
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