Match the given information with the equation for the line.
A line that has a slope of 53 and a y-intercept of -4.
A line that contains the y-intercept (0, -2) and a slope of −34
A line that contains the point (0, -8) with a slope of 32
A line that contains the points (0, -2) and (4, 0).
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
1) A line with a slope of 53 and a y-intercept of -4:
Equation: y = 53x - 4
2) A line with a y-intercept of (0, -2) and a slope of -34:
Equation: y = -34x - 2
3) A line that contains the point (0, -8) with a slope of 32:
Equation: y = 32x - 8
4) A line that contains the points (0, -2) and (4, 0):
First, calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1)
slope = (0 - (-2)) / (4 - 0) = 2 / 4 = 1/2
Next, use the point-slope form of a line to find the equation: y - y1 = m(x - x1)
Using the point (0, -2):
Equation: y - (-2) = (1/2)(x - 0)
Simplifying gives: y + 2 = (1/2)x
Rearranging gives the final equation: y = (1/2)x - 2