5 Problems - SHOW ALL WORK!
1. Solve for y:
2y + 4x = 12
2. Solve for y:
5x - y = 9
3. Find the slope of a line perpendicular to each given line.
a. Y = -1/2x - 2
b. y + 7 = 5/2(4x + 6)
4. Write the slope- intercept form of the equation of each line:
a. y - 4 = 5(x + 2)
b. 8x - 7y = 17
1. To solve for y in the equation 2y + 4x = 12, we need to isolate y.
First, subtract 4x from both sides of the equation:
2y = 12 - 4x
Next, divide both sides of the equation by 2 to solve for y:
y = (12 - 4x) / 2
y = 6 - 2x
So the solution for y is y = 6 - 2x.
2. To solve for y in the equation 5x - y = 9, we need to isolate y.
First, subtract 5x from both sides of the equation:
-y = 9 - 5x
Next, multiply both sides of the equation by -1 to solve for y:
y = -9 + 5x
So the solution for y is y = -9 + 5x.
3a. To find the slope of a line perpendicular to the equation y = -1/2x - 2, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. Therefore, the slope of the given line is -1/2.
To find the slope of a line perpendicular to the given line, we take the negative reciprocal of the slope. Therefore, the slope of the perpendicular line is 2.
3b. To find the slope of a line perpendicular to the equation y + 7 = 5/2(4x + 6), we need to determine the slope of the given line. First, simplify the equation:
y + 7 = 5/2 * 4x + 5/2 * 6
y + 7 = 10x + 15
Next, subtract 7 from both sides of the equation:
y = 10x + 15 - 7
y = 10x + 8
The slope-intercept form of a line is y = mx + b, where m is the slope. Therefore, the slope of the given line is 10.
To find the slope of a line perpendicular to the given line, we take the negative reciprocal of the slope. Therefore, the slope of the perpendicular line is -1/10.
4a. To write the slope-intercept form of the equation of the line given y - 4 = 5(x + 2), we need to isolate y.
First, distribute the 5 to the terms inside the parentheses:
y - 4 = 5x + 10
Next, add 4 to both sides of the equation:
y = 5x + 10 + 4
y = 5x + 14
So the slope-intercept form of the equation of the line is y = 5x + 14.
4b. To write the slope-intercept form of the equation of the line given 8x - 7y = 17, we need to isolate y.
First, subtract 8x from both sides of the equation:
-7y = -8x + 17
Next, divide both sides of the equation by -7 to solve for y:
y = (-8x + 17) / -7
So the slope-intercept form of the equation of the line is y = (-8x + 17) / -7.