How are you supposed to write an equation for the line that is parallel to the given line and that passes through the given point? For ex., what do you do for y = 3/4 x - 9, (-8,-18)?
since the line is parallel to the old one, the slope of the new one must be the same as the slope of the old one.
that is,
the new equation must be
y = (3/4)x + b
plug in the given point to find b,
put b back in the above equation and you are done.
thanks..in your opinion, is the way you did easier than doing it with point-slope form?
To find the equation of a line that is parallel to a given line and passes through a given point, you need to follow these steps:
Step 1: Determine the slope of the given line.
For the given line, y = (3/4)x - 9, the slope is 3/4.
Step 2: Use the slope to determine the slope of the parallel line.
Since parallel lines have the same slope, the parallel line will also have a slope of 3/4.
Step 3: Use the given point and the found slope to write the equation of the line using the point-slope form.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where x1 and y1 are the coordinates of the given point, and m is the slope of the line, substitute the values:
y - (-18) = (3/4)(x - (-8))
Step 4: Simplify the equation.
y + 18 = (3/4)(x + 8)
Step 5: Convert the equation to slope-intercept form (y = mx + b).
Distribute (3/4)(x + 8) and simplify:
y + 18 = (3/4)x + 6
y = (3/4)x + 6 - 18
y = (3/4)x - 12
Thus, the equation of the line that is parallel to y = (3/4)x - 9 and passes through the point (-8, -18) is y = (3/4)x - 12.
To write an equation for a line that is parallel to the given line and passes through a given point, you need to follow a few steps:
Step 1: Understand the given line equation.
For the given line equation, y = (3/4)x - 9, we can notice that the slope of the line is 3/4. The equation is in the form y = mx + b, where m represents the slope.
Step 2: Find the slope of the parallel line.
Since we want a line that is parallel to the given line, it will have the same slope. So, the slope of the parallel line will also be 3/4.
Step 3: Use the point-slope form of the line to write the equation.
The point-slope form of a line is y - y₁ = m(x - x₁), where (x₁, y₁) represents the coordinates of the given point and m is the slope. We'll substitute the values to form the line equation.
Using the given point (-8, -18) and the slope 3/4, we can write the equation as follows:
y - (-18) = (3/4)(x - (-8))
Simplifying, we have:
y + 18 = (3/4)(x + 8)
This is the equation for the line that is parallel to y = (3/4)x - 9 and passes through the point (-8, -18).