Use the image to answer the 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)
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To determine the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's find the slope of the line. The slope is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line.
Using the given points, (0, 4) and (1, 8), we can substitute these values into the formula:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
So the slope of the line is 4.
Next, we can use the point-slope form of a linear equation to write the equation of the line:
y - y₁ = m(x - x₁)
Substituting the slope (m = 4) and one of the points (0, 4), we have:
y - 4 = 4(x - 0)
Simplifying:
y - 4 = 4x
Lastly, we can rearrange the equation to the slope-intercept form, which is y = mx + b, where b is the y-intercept. Adding 4 to both sides, we get:
y = 4x + 4
So the equation of the line in slope-intercept form is y = 4x + 4.
To derive the equation of the line in slope-intercept form, we need two pieces of information: the slope of the line and the y-intercept.
1. First, let's find the slope of the line using the coordinates of the two plotted points (0, 4) and (1, 8). The slope formula is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the values (0, 4) and (1, 8) into the formula, we have:
slope = (8 - 4) / (1 - 0)
slope = 4 / 1
slope = 4
So, the slope of the line is 4.
2. Next, let's find the y-intercept. The y-intercept is the point where the line intersects the y-axis. From the graph, we can see that the y-intercept is (0, 4).
3. Now, we can write the equation of the line in slope-intercept form, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the values, we have:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.