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
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
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