Graphing Equations Practice

Question

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Question
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An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.

Derive the equation of the line in slope-intercept form.

(1 point)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope $m$ and the y-intercept $b$ of the line.

1. Calculate the slope (m): The slope $m$ is determined by the formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$ Using the points (0, 4) and (1, 8):

   • $(x_1,y_1)=(0,4)$
   • $(x_2,y_2)=(1,8)$

   Substituting these values into the formula gives: $$m=\frac{8-4}{1-0}=\frac{4}{1}=4$$

2. Determine the y-intercept (b): The y-intercept $b$ is the value of $y$ when $x=0$. From the point (0, 4), we see that: $$b=4$$

3. Write the equation: Now that we have $m=4$ and $b=4$, we can write the equation in slope-intercept form: $$y=4x+4$$

Thus, the equation of the line in slope-intercept form is: $$\boxed{{\displaystyle y=4x+4}}$$