How do you write an equation for the line that is parallel to the given line and that passes through the given point: y=-3x;(3,0)
I know how to do this using point-slope form, but not with slope intercept form..
very simple
your new equation must be
y = -3x + b , (the slope has to be the same, so the -3x part stays the same)
sub in the given point (3,0)
0 = -3(3) + b
b = 9
so y = -3x + 9
Angie
thanks, Reiny.
Emily, what about Angie?
To write an equation for a line that is parallel to a given line and passes through a given point, you can use either the point-slope form or the slope-intercept form. Let's see how we can do this using both methods.
Method 1: Point-slope form.
1. Start with the given line equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
2. Determine the slope of the given line since the parallel line will have the same slope. In this case, the slope of the given line is -3.
3. Now, use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point.
4. Plug in the values for the given point (3, 0) and the slope (-3) into the point-slope form equation.
y - 0 = -3(x - 3)
5. Simplify the equation to get the final answer: y = -3x + 9.
Method 2: Slope-intercept form.
1. Start with the given line equation in the form y = mx + b.
2. Identify the slope of the given line. In this case, the slope is -3.
3. Since the parallel line will have the same slope, the newly formed line will also have a slope of -3.
4. Use the given point (3, 0) to determine the y-intercept (b) of the line in the slope-intercept form equation.
Plug in the values of x = 3 and y = 0, and the slope (m = -3) into the equation: 0 = -3(3) + b.
5. Solve the equation to find the value of b: 0 = -9 + b.
By isolating b on one side of the equation, we find that b = 9.
6. Now that you have the slope (m = -3) and the y-intercept (b = 9), you can write the equation in slope-intercept form: y = -3x + 9.
Both methods will give you the same result: y = -3x + 9.