what is the slope-intercept form of the linear equation whose graph passes through (-2,4) and is parallel to the graph 3x+y=6?

a) y =-3x - 2
b) y =-3x + 10
c) y = 3x - 2
d) y = 3x + 10

which linear equation represents a line that passes through (3,-7) and has a slope of -4?

a) y = -4x-19
b) y = -4x-5
c) y = -4x+5
d) y = -4x+19

what is the slope of the line

y = -3 x + 6
?

using that slope:
(y - 4) / (x + 2)= slope
solve for y
=================================
y = -4 x + b
-7 = -4(3) + b
b = 5
so
y = -4 x + 5

You absolutely have to be able to do these - practice !!!!!!

To find the slope-intercept form of a linear equation, first, determine the slope of the given line. For a line parallel to the given line, the slope will be the same. Then, substitute the coordinates of the given point into the equation and solve for the y-intercept.

For the first question, the given equation is 3x + y = 6. To find the slope, rearrange the equation in the form y = mx + b (slope-intercept form), where m represents the slope. Subtract 3x from both sides to isolate y:

y = -3x + 6

From the equation, it can be determined that the slope is -3. Since the line being sought is parallel to this line, the slope will also be -3.

Now substitute the given point (-2, 4) into the slope-intercept form, y = -3x + b, and solve for the y-intercept, b. Substitute the values into the equation:

4 = -3(-2) + b
4 = 6 + b
4 - 6 = b
-2 = b

Therefore, the equation of the line that passes through (-2, 4) and is parallel to 3x + y = 6 is y = -3x - 2. Therefore, option a) y = -3x - 2 is the correct answer.

For the second question, the equation represents a line with a slope of -4 passing through the point (3, -7). Using the slope-intercept form, substitute the given values into the equation y = mx + b and solve for the y-intercept, b:

-7 = -4(3) + b
-7 = -12 + b
-7 + 12 = b
5 = b

Therefore, the equation of the line that passes through (3, -7) with a slope of -4 is y = -4x + 5. Therefore, option c) y = -4x + 5 is the correct answer.