Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 4 right parenthesis and left parenthesis 2 comma 8 right parenthesis.
The line passes through the points (1,4) and (2,8).
The line on the graph passes through the points (1,4) and (2,8). To find the equation of this line, we can use the slope-intercept form, which is given by y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates (1,4) and (2,8):
m = (8 - 4) / (2 - 1)
m = 4 / 1
m = 4
Now that we have the slope, we can find the y-intercept (b) by substituting one of the points into the slope-intercept form:
4 = 4(1) + b
4 = 4 + b
b = 4 - 4
b = 0
Therefore, the equation of the line is y = 4x + 0, which simplifies to y = 4x.
Based on the given information and the image, we can determine the equation of the line by using the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Given that the line passes through the points (1, 4) and (2, 8), we can substitute the values into the formula:
m = (8 - 4) / (2 - 1)
m = 4 / 1
m = 4
Now that we have the slope, we can use one of the given points and substitute it into the equation y = mx + b to find the y-intercept (b).
Using the point (1, 4):
4 = 4(1) + b
4 = 4 + b
b = 0
Therefore, the equation of the line passing through the points (1, 4) and (2, 8) is y = 4x + 0, which simplifies to y = 4x.
In the given coordinate plane, the line that passes through the points (1, 4) and (2, 8) is represented by an upward-slanting line with the equation y = 4x.