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.
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
To find the equation of the line, we can use the formula for the slope-intercept form, which is y = mx + b, where m represents the slope of the line.
We are given two points on the line, (1, 4) and (2, 8). We can use these points to find the slope of the line.
The slope, m, of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Using the coordinates (1, 4) and (2, 8):
m = (8 - 4)/(2 - 1) = 4/1 = 4
Therefore, the slope of the line is 4.
Since the line passes through the origin (0, 0), we can substitute the coordinates (0, 0) into the equation y = mx + b to find the y-intercept, b:
0 = 4(0) + b
0 = 0 + b
b = 0
Therefore, the equation of the line y = mx that describes the proportional relationship shown in the graph is y = 4x.
thats not right
Apologies for the incorrect response. Let's find the correct equation.
We are given two points on the line: (1, 4) and (2, 8). To find the equation of the line in slope-intercept form (y = mx + b), we need to find the slope, m, and the y-intercept, b.
The slope, m, of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Using the coordinates (1, 4) and (2, 8):
m = (8 - 4)/(2 - 1) = 4/1 = 4
The slope of the line is 4.
To find the y-intercept, b, we substitute the coordinates (1, 4) into the equation y = mx + b:
4 = 4(1) + b
4 = 4 + b
b = 0
The y-intercept, b, is 0.
Therefore, the equation of the line y = mx that describes the proportional relationship shown in the graph is y = 4x.
To find the equation of the line y = mx through the origin, we need to determine the slope of the line. The slope of a line is given by the formula:
m = (y2 - y1) / (x2 - x1)
From the given information, we have two points on the line: (1, 4) and (2, 8). Now we can substitute these values into the slope formula:
m = (8 - 4) / (2 - 1)
= 4 / 1
= 4
So, the slope of the line is 4.
Since the line passes through the origin (0,0), we can substitute the value of the slope (m) into the equation y = mx:
y = 4x
Therefore, the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph is y = 4x.