Write the equation of each line using the given information.
a. The points (−4,1) and (2,4) both lie on the line.
b. m=−1 and the point (2,−1) lies on the line.
c. It has the same slope as y=5 and passes through (1,1).
d. m=−3 and it has a y-intercept of (0,8).
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thats so helpful X_X
a. To find the equation of a line when two points are given, we can use the point-slope form of a linear equation. The formula is given as:
y - y1 = m(x - x1)
Given the points (−4,1) and (2,4), we can plug in the values into the formula:
y - 1 = m(x - (-4))
Simplifying further:
y - 1 = m(x + 4)
Now, we need to find the value of m (slope). We can use the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
m = (4 - 1) / (2 - (-4))
m = 3 / 6
m = 1/2
Substituting the slope value into the equation, we have:
y - 1 = (1/2)(x + 4)
b. Given that the slope (m) is -1 and the point (2,-1) lies on the line, we can use the point-slope form of a linear equation again:
y - y1 = m(x - x1)
Plugging in the values:
y - (-1) = -1(x - 2)
Simplifying further:
y + 1 = -x + 2
We can rearrange the equation to slope-intercept form:
y = -x + 1
c. In this case, the line has the same slope as y = 5 and passes through the point (1,1).
Since the slope is already given (5), we can proceed to the point-slope form:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 1 = 5(x - 1)
Expanding further:
y - 1 = 5x - 5
Moving the constant term to the other side:
y = 5x - 4
d. Given that the slope (m) is -3 and the y-intercept is (0,8), we can directly use the slope-intercept form of a linear equation:
y = mx + b
Plugging in the values:
y = -3x + 8
So, the equation of each line is:
a. y - 1 = (1/2)(x + 4)
b. y + 1 = -x + 2
c. y = 5x - 4
d. y = -3x + 8
a,b the point-slope form:
y-k = m(x-h)
c. y=1
d. y = mx+b
If those don't look familiar, you will never pass your test