Match the given information with the equation for the line. (4 points)
A line that contains the points (0, -2) and (4, 0). -
A line that has a slope of 5/3 and a y-intercept of -4. -
A line that contains the -intercept (0, -2) and a slope of -3/4. -
A line that contains the point (0, -8) with a slope of 3/2. -
Word bank:
-5x+3y=-12
y=3/2x-8
y=-3/4x-2
2y-x=-4
A line that contains the points (0, -2) and (4, 0). - 2y-x=-4
A line that has a slope of 5/3 and a y-intercept of -4. - y=3/2x-8
A line that contains the x-intercept (0, -2) and a slope of -3/4. - y=-3/4x-2
A line that contains the point (0, -8) with a slope of 3/2. - y=3/2x-8
Bot you’re wrong, you can only us the words in the word bank once
Apologies for the mistake. Here is the correct matching:
A line that contains the points (0, -2) and (4, 0). - 2y-x=-4
A line that has a slope of 5/3 and a y-intercept of -4. - y=3/2x-8
A line that contains the x-intercept (0, -2) and a slope of -3/4. - -5x+3y=-12
A line that contains the point (0, -8) with a slope of 3/2. - y=-3/4x-2
To match the given information with the equation for the line, we need to determine the slope and the y-intercept of each line.
1. A line that contains the points (0, -2) and (4, 0).
To find the slope (m) of the line using the two points, we use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values, we get:
m = (0 - (-2)) / (4 - 0) = 2/4 = 1/2
Now, we can use the point-slope form of a line to find the equation:
y - y₁ = m(x - x₁)
Substituting one of the given points into the equation:
y - (-2) = (1/2)(x - 0)
Simplifying:
y + 2 = (1/2)x
y = (1/2)x - 2
So, the equation for the first line is y = (1/2)x - 2.
2. A line that has a slope of 5/3 and a y-intercept of -4.
Since we are given the slope and the y-intercept, we can directly write the equation in slope-intercept form as:
y = mx + b
y = (5/3)x - 4
So, the equation for the second line is y = (5/3)x - 4.
3. A line that contains the y-intercept (0, -2) and a slope of -3/4.
Again, we have the slope and the y-intercept, allowing us to write the equation directly in slope-intercept form:
y = mx + b
y = (-3/4)x - 2
Therefore, the equation for the third line is y = (-3/4)x - 2.
4. A line that contains the point (0, -8) with a slope of 3/2.
Using the point-slope form of a line, we have:
y - y₁ = m(x - x₁)
Substituting the values:
y - (-8) = (3/2)(x - 0)
Simplifying:
y + 8 = (3/2)x
y = (3/2)x - 8
Hence, the equation for the fourth line is y = (3/2)x - 8.
Therefore, matching the given information with the equations for the lines, we have:
1. A line that contains the points (0, -2) and (4, 0) corresponds to the equation: y = (1/2)x - 2.
2. A line that has a slope of 5/3 and a y-intercept of -4 corresponds to the equation: y = (5/3)x - 4.
3. A line that contains the y-intercept (0, -2) and a slope of -3/4 corresponds to the equation: y = (-3/4)x - 2.
4. A line that contains the point (0, -8) with a slope of 3/2 corresponds to the equation: y = (3/2)x - 8.