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Chapter 1: Problem 13

Graph of a linear function Find and graph the linear function that passes through the points (1,3) and (2,5)

Short Answer

Expert verified
Answer: The equation of the linear function that passes through the points (1,3) and (2,5) is y = 2x + 1. To graph it, plot the y-intercept (0, 1) on the graph, use the slope 2 to find another point by going up 2 units and right 1 unit from the y-intercept point, and connect the points with a straight line.

Step by step solution

01

Find the slope

To find the slope of the line, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) is the first point (1,3) and (x2, y2) is the second point (2,5). Plugging in the given points, we have: m = (5 - 3) / (2 - 1)
02

Solve for the slope

Calculating the slope with the values given: m = (5 - 3) / (2 - 1) = 2 / 1 = 2 So, the slope of the linear function is 2.
03

Find the equation of the line

Now we have the slope and one of the points. We can use the point-slope form of the line to find the equation of the line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points. Using the first point (1,3) and the slope 2, we get: y - 3 = 2(x - 1)
04

Solve for y

We can rewrite the equation of the line in slope-intercept form (y = mx + b) by solving for y: y - 3 = 2(x - 1) y - 3 = 2x - 2 y = 2x + 1 So, the equation of the linear function is y = 2x + 1.
05

Graph the linear function

To graph the linear function y = 2x + 1, follow these steps: 1. Plot the y-intercept (0, 1) on the graph. 2. Use the slope 2 to find another point by going up 2 units and right 1 unit from the y-intercept point. 3. Connect the points with a straight line. After graphing, you will find a straight line that passes through the points (1,3) and (2,5), representing the linear function y = 2x + 1.

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