Steph has a line drawn on her paper with the equation y = 4x - 3. She wants to draw a line parallel to the given line, but through the point (2, 2). Describe, in words, the steps she needs to go through to find the equation of this new line.
slope of both lines = m = 4
find a line of form y =4 x + b through (2,2) by substituting 2 for x and 2 for y and solving for b
Petra needs to find the equation of a line through (–2, 3) that is parallel to the line represented by y = 2x– 4. Which equation best represents Petra's equation?
To find the equation of a line parallel to the given line, but passing through a specific point, Steph needs to follow these steps:
Step 1: Understand the concept
First, it is important to understand that parallel lines have equal slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope. Hence, to find the equation of a line parallel to the given line, the new line must have the same slope as the given line.
Step 2: Determine the slope of the given line
The equation of the given line is y = 4x - 3. By comparing it with the slope-intercept form, we can determine that the slope of the given line is 4.
Step 3: Use the slope-intercept form
Since Steph wants to find the equation of a line passing through the point (2, 2), she can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 4: Substitute the values
Substitute the slope value and the coordinate values (x = 2, y = 2) into the equation y = mx + b to find the value of b, which represents the y-intercept of the new line. In this case, we have:
2 = 4(2) + b
Simplify the equation:
2 = 8 + b
Step 5: Solve for b
To solve for b, we need to isolate it. Subtract 8 from both sides of the equation:
2 - 8 = 8 + b - 8
-6 = b
So, b = -6
Step 6: Write the equation of the new line
Now that we have the slope (m = 4) and the y-intercept (b = -6), we can write the equation of the new line. Hence, the equation of the line parallel to the given line, but passing through the point (2, 2), is:
y = 4x - 6