What is an equation of the line that passes through the points (4,-6) and has a slope of -3
1 answer:
Answer:
1) y = -3x + 6
Step-by-step explanation:
1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula and substitute values for
,
, and
.
Since represents the slope, substitute -3 in its place. Since
and
represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:
2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.
So, the first option is correct.
You might be interested in
Answer:
1. Translation: g(x) = f(x-a)+b.
2. Reflection around y-axis: h(x) = f(-x)
3. Reflection around x-axis: k(x) = -f(x)
4. Rotation of 90° :
5. Rotation of 180° : .
6. Rotation of 270° : .
Step-by-step explanation:
Let us assume that the transformations namely translation, reflection are applied to a function f(x) and the rotation is applied to the point ( x,y ).
So, according to the options:
We know that 'translation moves the image in horizontal and vertical direction'.
1. As we have to translate the function f(x) 'a' units to the right and 'b' units up. So, the new form of the function becomes g(x) = f(x-a)+b.
Further, we know that 'reflection means to flip the image around a line'.
2. As, we have to reflect the function f(x) around y-axis. The new form of the function is h(x) = f(-x).
3. As, we have to reflect the function f(x) around x-axis. The new form of the function is k(x) = -f(x).
Since, 'rotation turns the image around a point to a certain degree'.
4. As, we have to rotate ( x,y ) counter-clockwise to 90° about the origin, the new form of the function is .
5. As, we have to rotate ( x,y ) counter-clockwise to 180° about the origin, the new form of the function is .
6. As, we have to rotate ( x,y ) counter-clockwise to 270° about the origin, the new form of the function is .