1. Write the equation for the horizontal line that contains point G(-8, 8).
2. What is an equation for the line that passes through points (-1, -4) and (1, 4)? Write the equation in slope-intersect form.
3. Write an equation for the vertical line that contains point E(10, -3).
#1.
Note that horizontal line has a zero slope, and in the form y = c, where c is a any real number.
Therefore, if it passes through the point (-8,8), the equation must be y = 8.
#2.
If we are given the two points on the line, we first get the slope using the formula
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are points on the line. Substituting,
m = (4 - (-4)) / (1 - (-1))
m = (4+4)/(1+1)
m = 4
Then we substitute it on the point slope formula:
y - y1 = m(x - x1)
Substituting,
y - 4 = 4(x - 1)
y = 4x - 4 + 4
y = 4x
#3.
Note that vertical line has a slope equal to infinity, and in the form x = c, where c is a any real number.
Therefore, if it passes through the point (10,-3), the equation must be x = 10.
Hope this helps :3
Thank You so much Jai
1. The equation for a horizontal line is of the form y = c, where c is the y-coordinate of any point on the line. Since point G(-8, 8) lies on the line, the equation for the horizontal line that contains point G(-8, 8) is y = 8.
2. To find the equation of the line passing through points (-1, -4) and (1, 4), we need to find both the slope (m) and the y-intercept (c). The slope of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
So, m = (4 - (-4)) / (1 - (-1))
= 8 / 2
= 4
Now, to find the y-intercept (c), we can use the slope-intercept form of a linear equation, which is y = mx + c. We can substitute the slope (m) and one of the given points (-1, -4) into the equation and solve for c.
-4 = 4(-1) + c
-4 = -4 + c
c = -4 + 4
c = 0
Therefore, the equation for the line passing through the points (-1, -4) and (1, 4) in slope-intercept form is y = 4x.
3. The equation for a vertical line is of the form x = c, where c is the x-coordinate of any point on the line. Since point E(10, -3) lies on the line, the equation for the vertical line that contains point E(10, -3) is x = 10.
To write the equations for the lines described in each question, we can use different forms of linear equations depending on the given information. Let's go through each question and explain the process of finding the equations step by step.
1. To write the equation for a horizontal line that contains the point G(-8, 8), we know that a horizontal line has a constant y-value for all x-values. Therefore, the equation will be in the form y = k, where k represents the constant y-value.
In this case, G(-8, 8) tells us that the line passes through the point (-8, 8). So the equation for the horizontal line is y = 8. That's it! Since the y-value remains constant at 8, the equation does not contain any variables.
2. To find the equation of a line that passes through the points (-1, -4) and (1, 4), we can use the slope-intercept form of a linear equation. The slope-intercept form is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
First, we need to calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Let's take the coordinates of the two points as (-1, -4) and (1, 4).
m = (4 - (-4)) / (1 - (-1))
m = 8 / 2
m = 4
Now that we have the slope, we can substitute it into the slope-intercept form of the equation and use one of the given points to find the y-intercept (b). Let's use the point (-1, -4).
-4 = 4(-1) + b
-4 = -4 + b
b = -4 + 4
b = 0
Substitute the values of m and b back into the equation y = mx + b to get the final equation:
y = 4x + 0
y = 4x
So, the equation in slope-intercept form for the line passing through the points (-1, -4) and (1, 4) is y = 4x.
3. To find the equation for a vertical line that contains the point E(10, -3), we know that a vertical line has a constant x-value for all y-values. Therefore, the equation will be in the form x = k, where k represents the constant x-value.
In this case, E(10, -3) tells us that the line passes through the point (10, -3). So the equation for the vertical line is x = 10. Similar to the first question, the x-value remains constant at 10 in this case.
To summarize:
1. The equation for the horizontal line that contains point G(-8, 8) is y = 8.
2. The equation for the line passing through points (-1, -4) and (1, 4) in slope-intercept form is y = 4x.
3. The equation for the vertical line that contains point E(10, -3) is x = 10.