5) Write an equation in point-slope form with the given: (5,-8),(5,8)
8) Write an equation in slope-intercept form for a line that passes through the point (2,-5) and is parallel to y = 11
: )
well, the slope is undefined; the line is vertical.
So, the line is x=5
The line y=11 has zero slope.
So, the line through (2,-5) is y = -5
To write an equation in point-slope form, we use the formula:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the given points are (5, -8) and (5, 8). Since the x-coordinates of both points are the same, we can conclude that the line is vertical. As a result, the slope is undefined.
So, the equation in point-slope form will be:
x = 5
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To write an equation in slope-intercept form, we use the formula:
y = mx + b
where m is the slope of the line and b is the y-intercept.
In this case, the line is parallel to y = 11, which means it has the same slope. Therefore, the slope (m) of the line is 11.
Now, let's find the y-intercept (b) of the line by substituting the coordinates (2, -5) into the equation:
y = mx + b
-5 = 11(2) + b
-5 = 22 + b
b = -27
So, the equation in slope-intercept form will be:
y = 11x - 27
To write an equation in point-slope form, you need to know the coordinates of a point on the line and the slope of the line.
For the first question, the given points are (5,-8) and (5,8). To find the slope, you can use the formula: m = (y2 - y1) / (x2 - x1). Substituting the coordinates, we get m = (8 - (-8)) / (5 - 5) = 16 / 0.
However, we can see that the denominator is 0, which means the slope is undefined. This implies that the line is vertical and parallel to the y-axis. The equation of a vertical line passing through the x-coordinate is x = a, where 'a' is the x-coordinate. Therefore, the equation is x = 5 in point-slope form.
For the second question, the given line y = 11 is parallel to the line we want to find the equation for. When two lines are parallel, they have the same slope. Hence, the slope of our line is also 11.
Using the slope-intercept form of a line, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept, we substitute the values we have. The given point is (2,-5), which means the value of 'x' is 2, and 'y' is -5.
Therefore, the equation becomes -5 = 11(2) + b. Simplifying it further, we have -5 = 22 + b. To isolate 'b', we subtract 22 from both sides, resulting in -27 = b.
Finally, the equation in slope-intercept form for the line that is parallel to y = 11 and passes through the point (2,-5) is y = 11x - 27.