Final answer:
To find the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept. We can solve each part of the question step-by-step to find the equations of the lines and then graph them together on the same set of axes.
Step-by-step explanation:
To find the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept. Let's solve each part of the question step-by-step:
a. To find the equation of the line going through (-5, -1) and (1, 2), we first need to calculate the slope:
Slope (m) = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
Slope (m) = (2 - (-1)) / (1 - (-5)) = 3/6 = 1/2
Now, we can use the slope and one of the given points to find the y-intercept:
y = mx + b
2 = (1/2)(1) + b
Simplifying, we get:
2 = 1/2 + b
b = 2 - 1/2 = 3/2
Therefore, the equation of the line is y = (1/2)x + 3/2.
b. To find the equation of a line perpendicular to the line found in part a and passing through (2, 4), we need to find the negative reciprocal of the slope of the line found in part a:
Slope of perpendicular line = -1 / (1/2) = -2
Using the slope and the given point (2, 4), we can find the y-intercept:
4 = (-2)(2) + b
Simplifying, we get:
4 = -4 + b
b = 8
Therefore, the equation of the perpendicular line is y = -2x + 8.
c. To graph both lines on the same set of axes, plot the points (-5, -1), (1, 2), and (2, 4). Then connect the points to form the lines.