Write an equation in slope-intercept form of the line that passed through (-3,4) and (1,4).
I think the answer is y=0/4x+4
Thank you
yes. Since both points have 4 for a y-coordinate, the line is horizontal:
y = 4
To find the equation of the line that passes through the points (-3,4) and (1,4), we can use the slope-intercept form of a linear equation, which is y = mx + b.
First, let's find the slope (m). The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-3,4) and (1,4), we plug in the values into the formula:
m = (4 - 4) / (1 - (-3))
Simplifying, we get:
m = 0 / 4
m = 0
Now, we know that the slope (m) is 0.
Next, let's find the y-intercept (b). We can choose either of the given points, let's use (-3,4). We can substitute these values into the slope-intercept form and solve for b:
4 = 0 * (-3) + b
4 = 0 + b
b = 4
Now, we have the slope (m = 0) and the y-intercept (b = 4).
Therefore, the equation of the line in slope-intercept form is:
y = 0x + 4
Simplifying, we get:
y = 4
Actually, the equation you provided, y = 0/4x + 4, is incorrect. To find the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept of the line.
To find the slope, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Given the points (-3, 4) and (1, 4), we can substitute these values into the formula:
m = (4 - 4) / (1 - (-3))
m = 0 / 4
m = 0
Since the y-coordinate remains constant (4) for both points, the slope is zero.
Now, let's find the y-intercept (b). We can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Using (-3, 4) as our point, we substitute the values into the equation:
4 = 0(-3) + b
4 = 0 + b
4 = b
Therefore, the y-intercept (b) is 4.
Now we have both the slope (m = 0) and the y-intercept (b = 4). Plugging these values into the slope-intercept form, we get the equation of the line:
y = 0x + 4
or simply:
y = 4
So, the correct equation in slope-intercept form for the line passing through (-3, 4) and (1, 4) is y = 4.