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Question

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)
Remaining Attempts : 3
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Answer 1

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

1. Find the slope ($m$): The slope of a line that passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ is calculated using the formula:

   $$m=\frac{y_2-y_1}{x_2-x_1}$$

   Using the points $(0,4)$ and $(1,8)$:

   $$m=\frac{8-4}{1-0}=\frac{4}{1}=4$$

2. Use the slope to find the y-intercept ($b$): We can use one of the points to solve for $b$. We'll use the point $(0,4)$:

   $$y=mx+b$$ $$4=4(0)+b$$ $$4=b$$

3. Write the equation: Now that we have both $m$ and $b$, we can write the equation in slope-intercept form:

   $$y=4x+4$$

Thus, the equation of the line is:

$$\boxed{{\displaystyle y=4x+4}}$$