Match the given information with the equation for the line.
A line that has a slope of 5/3 and a y-intercept of -4.
A line that contains the y-intercept (0, -2) and a slope of −3/4
A line that contains the point (0, -8) with a slope of 3/2
A line that contains the points (0, -2) and (4, 0).
Choices:
2y - x= -4
y= 3/2x -8
-5x + 3y = -12
y = -3/4x - 2
A line that has a slope of 5/3 and a y-intercept of -4: y = 5/3x - 4
A line that contains the y-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
A line that contains the points (0, -2) and (4, 0): y = -3/4x - 2
are you sure?
Apologies for the confusion. Let me match the information with the correct equations:
A line that has a slope of 5/3 and a y-intercept of -4: y = 5/3x - 4
A line that contains the y-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
A line that contains the points (0, -2) and (4, 0): y = 2x - 2
To match the given information with the equation for the line, we will use the slope-intercept form of a linear equation, which is y = mx + b.
1. A line that has a slope of 5/3 and a y-intercept of -4:
We can directly match this information to the slope-intercept form. The slope (m) is 5/3, and the y-intercept (b) is -4. Therefore, we can write the equation as y = 5/3x - 4.
2. A line that contains the y-intercept (0, -2) and a slope of -3/4:
Again, we can match this information to the slope-intercept form. The slope (m) is -3/4, and the y-intercept (b) is -2. Therefore, we can write the equation as y = -3/4x - 2.
3. A line that contains the point (0, -8) with a slope of 3/2:
To find the equation, we need to use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Using the values from the given information, the point is (0, -8), and the slope (m) is 3/2. Substituting these values into the point-slope equation, we get y - (-8) = (3/2)(x - 0). Simplifying gives us y + 8 = (3/2)x. To put it in slope-intercept form, we can rewrite it as y = (3/2)x - 8.
4. A line that contains the points (0, -2) and (4, 0):
To find the equation, we can first calculate the slope (m) using the formula (change in y) / (change in x) = (y2 - y1) / (x2 - x1). Taking the first point as (x1, y1) and the second point as (x2, y2), we have (0 - (-2)) / (4 - 0) = 2/4 = 1/2. Therefore, the slope (m) is 1/2. Now, we can use either of the given points and the slope to find the equation using the point-slope form. Let's use the point (0, -2). The equation will be y - (-2) = (1/2)(x - 0). Simplifying gives us y + 2 = (1/2)x. To put it in slope-intercept form, we can rewrite it as y = (1/2)x - 2.
Matching the given information with the equation for the line:
1. A line that has a slope of 5/3 and a y-intercept of -4:
Equation: y = 5/3x - 4
2. A line that contains the y-intercept (0, -2) and a slope of -3/4:
Equation: y = -3/4x - 2
3. A line that contains the point (0, -8) with a slope of 3/2:
Equation: y = 3/2x - 8
4. A line that contains the points (0, -2) and (4, 0):
Equation: y = 1/2x - 2