Q55. Write an equation in slope-inter... [FREE SOLUTION]

Chapter 12: Q55. (page 637)

Write an equation in slope-intercept form for each graph.

Short Answer

Expert verified

The equation of the graph in slope-intercept form is $y = \frac{2}{3} x + \frac{1}{3}$ .

Step by step solution

Step 1. Given Information.

From the given graph, the line passes through $(4, 3)$ and $(- 2, - 1)$ . The equation of the line in slope-intercept form is to be determined.

Step 2. Calculation.

The equation of a line in slope-intercept form is y=mx+b, where m is the slope of the line and b is the y-intercept.

The slope of a line passing through two points is given by:

$\begin{array}{l} m = \frac{y_{2} 鈭� y_{1}}{x_{2} 鈭� x_{1}} \\ m = \frac{鈭� 1 鈭� 3}{鈭� 2 鈭� 4} \\ m = \frac{鈭� 4}{鈭� 6} \\ m = \frac{2}{3} \end{array}$

The equation of a line with slope m and passing through a point is given by:

$\begin{array}{l} y 鈭� y_{1} = m (x 鈭� x_{1}) \\ y 鈭� 3 = \frac{2}{3} (x 鈭� 4) \\ y 鈭� 3 = \frac{2}{3} x 鈭� \frac{8}{3} \\ y = \frac{2}{3} x 鈭� \frac{8}{3} + 3 \\ y = \frac{2}{3} x + \frac{1}{3} \end{array}$

Step 3. Conclusion.

Hence, the equation of the graph in slope-intercept form is $y = \frac{2}{3} x + \frac{1}{3}$ .

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91影视

Write an equation in slope-intercept form for each graph.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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