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Chapter 1: Problem 23

Find the slope and \(y\) -intercept (if possible) of the equation of the line. Sketch the line. $$7 x-6 y=30$$

Short Answer

Expert verified
The slope of the line is \(\frac{7}{6}\) and the y-intercept is -5.

Step by step solution

01

Conversion to slope-intercept form

Start with the equation and transform it into the slope-intercept form (i.e., \(y = mx + c\)), for which the coefficients of \(x\) and \(y\) (i.e., \(m\) and \(c\)) are the slope and y-intercept of the line respectively. The given equation, \(7x-6y = 30\), becomes \(y = \frac{7}{6}x - 5\) after isolating \(y\), where it is apparent that \(m = \frac{7}{6}\) and \(c = -5\).
02

Identify the Slope and Y-intercept

The slope of the line \(m\) is the coefficient of \(x\), which is \(\frac{7}{6}\). The y-intercept \(c\) is the constant term, which is -5.
03

Sketch the Line

To sketch the line, first draw a cartesian coordinate system. Center the graph at the y-intercept which is at point (0,-5) on the y-axis. From this point, use the slope \(m = \frac{7}{6}\) as a ratio of change in \(y\) for every change in \(x\), that is 7 units up for every 6 units to the right. Plot the line over several points and connect the dots to form a straight line.

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Most popular questions from this chapter

A company produces a product for which the variable cost is 12.30 dollars per unit and the fixed costs are 98,000 dollars. The product sells for 17.98 dollars. Let \(x\) be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost \(C\) as a function of the number of units produced. (b) Write the revenue \(R\) as a function of the number of units sold. (c) Write the profit \(P\) as a function of the number of units sold. (Note: \(P=R-C\) ).

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