What is the equation of the line that passes through the points (−3,4) and (−6,3) ? Write the answer in slope-intercept form.
To find the equation of the line that passes through the points (−3,4) and (−6,3), we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-3, 4) and (x2, y2) = (-6, 3).
m = (3 - 4) / (-6 - (-3))
m = (-1) / (-3)
m = 1/3
So the slope of the line is 1/3.
Now that we have the slope, we can use one of the given points (−3,4) and the slope-intercept form to find the y-intercept (b).
Using the point (−3,4), we have:
4 = (1/3)(-3) + b
4 = -1 + b
b = 5
So the y-intercept is 5.
Now, we have the slope (1/3) and the y-intercept (5), so we can write the equation of the line in slope-intercept form:
y = (1/3)x + 5
y = (1/3)x + 5
check
does that go through ( -6 , 3 ) ?????
y = (1/3) * ( -6) + 5 ??????
y = -2 + 5
y = 3
ok :)
Yes! Plugging in the x-coordinate of -6 into the equation y = (1/3)x + 5 gives you y = 3, which matches the y-coordinate of -6, 3. Therefore, the line does indeed pass through the point (-6,3).
To find the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
The slope (m) of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Given the points (-3, 4) and (-6, 3), we can calculate the slope as:
m = (3 - 4) / (-6 - (-3))
m = (-1) / (-3)
m = 1/3
Now, let's find the y-intercept (b). We can choose any of the two points to substitute into the equation y = mx + b. Let's use the point (-3, 4):
4 = (1/3)(-3) + b
4 = -1 + b
b = 4 + 1
b = 5
Therefore, the equation of the line passing through the points (-3, 4) and (-6, 3) in slope-intercept form is:
y = (1/3)x + 5