Write an equation given form of the line passing through the given points.
1. Slope-Intercept form, passing through (-3,4) and (1,4)
2. Point-Slope form, passing through (-3,1) and slope 2.
1. To find the equation in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-3,4) and (1,4), we have:
m = (4 - 4) / (1 - (-3))
m = 0 / 4
m = 0
Since the y-values are the same for both points, the slope is 0.
Next, let's find the y-intercept (b) using the point (-3,4). We can substitute the values (-3,4) and the slope (0) into the slope-intercept form (y = mx + b) to solve for b:
4 = 0*(-3) + b
4 = 0 + b
b = 4
Therefore, the equation of the line passing through (-3,4) and (1,4) in slope-intercept form is:
y = 0x + 4
Simplified: y = 4
2. To write the equation of the line in point-slope form, we need to use the formula:
y - y1 = m(x - x1)
Using the point (-3,1) and the slope 2, we have:
y - 1 = 2(x - (-3))
y - 1 = 2(x + 3)
Therefore, the equation of the line passing through (-3,1) with a slope of 2 in point-slope form is:
y - 1 = 2(x + 3)
What are the x- and y-intercepts for the graph of -2x+7y=14
x-intercept:
To find the x-intercept, we need to set y = 0 in the equation -2x + 7y = 14 and solve for x.
-2x + 7(0) = 14
-2x = 14
x = 14 / -2
x = -7
Therefore, the x-intercept is -7.
y-intercept:
To find the y-intercept, we need to set x = 0 in the equation -2x + 7y = 14 and solve for y.
-2(0) + 7y = 14
7y = 14
y = 14 / 7
y = 2
Therefore, the y-intercept is 2.
What does the graph of x=7 look like?
a. Vertical line passing the y-axis at 7
b. Vertical line passing the x-axis at 7
c. Horizontal line passing the y-axis at 7
d. Horizontal line passing the x-axis at 7
The graph of x=7 is a vertical line passing through the x-axis at the value of 7.
Therefore, the correct answer is b. Vertical line passing the x-axis at 7.
Write y=1/3x+2 in standard form using integers.
To write the equation y=1/3x+2 in standard form using integers, we need to eliminate the fraction and rearrange the terms.
First, let's multiply the entire equation by 3 to eliminate the fraction:
3y = 3(1/3x) + 3(2)
3y = x + 6
Next, let's rearrange the equation so that the x and y terms are on the same side and the constant term is on the other side:
x - 3y = -6
Therefore, the equation y=1/3x+2 in standard form using integers is x - 3y = -6.
a. y=5x-2 passing through (2,-1)
slope-intercept form y=mx+b
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).
First, let's find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Using the point (2, -1), we have:
x1 = 2
y1 = -1
Next, let's find the slope by substituting the coordinates into the formula:
m = (-1 - y1) / (2 - x1)
m = (-1 - (-1)) / (2 - 2)
m = 0 / 0
Since we have a division by zero, we need to use an alternative method to find the slope. Since the line is in the form y = 5x - 2, we can see that the slope is 5.
Now, let's find the y-intercept (b) by substituting the coordinates into the slope-intercept form:
-1 = 5(2) + b
-1 = 10 + b
b = -1 - 10
b = -11
Therefore, the equation of the line y=5x-2 passing through (2,-1) in slope-intercept form is:
y = 5x - 11
y=9x passing through (0, -5)
slope-intercept form y=mx+b