Find the equation of the line and write your answer in the slope-intercept form.
1. Has a y-intercept of 5 and a slope of
2. Has a slope of -5 and a y-intercept of 2/3.
3. Has a slope of -3 and contains (4,9).
4. Has a slope of 4/9 and contains (0,-2)
5. Contains the points (4,5) and (6,12).
the slope-y intercept equation has the form
y = mx + b , where m is the slope and b is the y-intercept
so for the first 2 questions it is simply a matter of putting in the given values
for the next two , we are given the slope but not the intercept
so for 3. start with
y = -3x + b
but (4,9) lies on it , so
9 = -3(4) + b
21 = b
equation is y = -3x + 21
Do #4 the same way
For #5 , first find the slope , then proceed just like I did in #3
1. To find the equation of a line with a y-intercept of 5 and a slope of "m," we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, "m" represents the slope and "b" represents the y-intercept.
So, for the first question, the equation would be y = mx + 5.
2. For the second question, we have a slope of -5 and a y-intercept of 2/3. Therefore, the equation becomes y = -5x + 2/3.
3. To find the equation of a line with a slope of -3 and containing the point (4,9), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Here, (x1, y1) represents the given point, and "m" represents the slope.
Plugging in the values, we get (x1, y1) = (4,9) and m = -3. Substituting these values into the equation, we have y - 9 = -3(x - 4). Simplifying further, we get y - 9 = -3x + 12. Rearranging the terms, the equation becomes y = -3x + 21.
4. For the fourth question, we are given a slope of 4/9 and a point (0,-2). Using the point-slope form, we substitute (x1, y1) = (0,-2) and m = 4/9 into the equation y - y1 = m(x - x1). Simplifying further, we get y - (-2) = (4/9)(x - 0). Simplified, this becomes y + 2 = (4/9)x. Rearranging, the equation in slope-intercept form is y = (4/9)x - 2.
5. To find the equation of a line containing the points (4,5) and (6,12), we can first find the slope, "m," using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.
Substituting the values, we get m = (12 - 5) / (6 - 4) = 7 / 2.
Now, using the point-slope form, we can choose either of the given points as (x1, y1) and the found slope as "m." Let's choose (4,5) as (x1, y1) and substitute these values into the equation y - y1 = m(x - x1). Simplifying further, we get y - 5 = (7/2)(x - 4). Expanding and rearranging the terms, the equation becomes y = (7/2)x - 9/2.
So, the equation of the line passing through the points (4,5) and (6,12) is y = (7/2)x - 9/2.