What method can be used to write the equation of a line in slope-intercept form given two points?
Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Catherine saved some money and plans to add the same amount each week to her savings account. The table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y.
Weeks, x
Dollars in account, y
4
74
6
86
9
104
11
116
Which linear equation represents Catherine’s situation?
y = one-sixth x + 70
y = 6 x + 50
y = StartFraction 1 Over 9 EndFraction x + 104
y = 11 x + 116
Using the two given points (4, 74) and (6, 86), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (86 - 74) / (6 - 4)
m = 12 / 2
m = 6
Now we have the slope and can use one of the points to find the y-intercept:
y = mx + b
74 = 6(4) + b
74 = 24 + b
b = 50
Therefore, the linear equation that represents Catherine's situation is:
y = 6x + 50
Which can be the first step in finding the equation of the line that passes through the points (5, negative 4) and (negative 1, 8) in slope-intercept form?
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2. This is the slope of the line passing through the two points.
Miguel volunteers at his local food pantry and takes note of how much money is donated each day during a 10-day fundraising phone-a-thon. Below is the graph that represents the data that he collected.
A graph titled Food Pantry Donations has number of days on the x-axis and dollars donated on the y-axis. A line goes through points (1, 75) and (2, 100).
The slope of the line that represents the data that Miguel collected is 25, and the y-intercept is 50. What do the slope and y-intercept represent in Miguel’s situation?
The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3.
She found the incorrect y-intercept in step 2.
The correct calculation in step 2 should be:
25 = -4(-7) + b
25 = 28 + b
b = -3
So the equation should be:
y = -4x - 3
Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the graph, then it must be the same function.
On a coordinate plane, a line goes through points (0, negative 1) and (2, 0).
Which equation proves Jeremy’s argument is incorrect?
y = negative one-half x minus 1
y = negative one-half x + 1
y = one-half x minus 1
y = one-half x + 1