Math Equation Response Question
A line is graphed below.
The line passes through the points (0, 3), (-1, 5), and (3, -3)
Write an equation in the form y = mx + b that represents this line.
Use the on-screen keyboard to type the correct equation in the box.
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There are several ways to find the equation of a line. One common method is to use the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (0, 3) and (-1, 5) to find the slope:
m = (5 - 3) / (-1 - 0) = 2 / -1 = -2
Next, we can choose any point on the line and substitute its coordinates (x, y) along with the slope into the slope-intercept form, y = mx + b, to find the value of b. Let's use the point (0, 3):
3 = -2 * 0 + b
3 = b
Therefore, the equation of the line is:
y = -2x + 3
To write an equation in the form y = mx + b, we need to find the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose the points (-1, 5) and (0, 3) to calculate the slope.
m = (5 - 3) / (-1 - 0)
m = 2 / -1
m = -2
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can use any of the given points. Let's use the point (0, 3).
Substitute the values of x (0) and y (3) and the slope (m) into the equation y = mx + b:
3 = -2(0) + b
3 = b
So, the y-intercept (b) of the line is 3.
Step 3: Write the equation
Now that we have the slope (m) and the y-intercept (b), we can write the equation y = mx + b.
Substituting the values of m and b:
y = -2x + 3
So, the equation that represents the line passing through the points (0, 3), (-1, 5), and (3, -3) is y = -2x + 3.
To find the equation of the line in the form y = mx + b, we need to determine the slope (m) and the y-intercept (b).
Step 1: Calculate the slope (m)
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-1, 5) and (0, 3), we can calculate the slope:
m = (3 - 5) / (0 - (-1))
m = -2 / 1
m = -2
Step 2: Find the y-intercept (b)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. We can determine it by substituting the coordinates of one of the given points into the equation y = mx + b and solving for b.
Using the point (0, 3), we have:
3 = -2(0) + b
3 = b
Step 3: Write the equation in the form y = mx + b
Now that we have the slope (m = -2) and the y-intercept (b = 3), we can write the equation of the line:
y = -2x + 3
Therefore, the equation in the form y = mx + b that represents the line passing through the points (0, 3), (-1, 5), and (3, -3) is:
y = -2x + 3