Question

For the equation y-7=-4(x+6), what is the slope-intercept form?

Answer 1

What is a point on the line?

Answer 2

To convert the equation \( y - 7 = -4(x + 6) \) to slope-intercept form, we need to solve for \( y \) in terms of \( x \).

1. Start with the equation:
\[
y - 7 = -4(x + 6)
\]

2. Distribute the \(-4\) on the right side:
\[
y - 7 = -4x - 24
\]

3. Add \( 7 \) to both sides to isolate \( y \):
\[
y = -4x - 24 + 7
\]
\[
y = -4x - 17
\]

Now the equation is in slope-intercept form, which is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.

Thus, the slope-intercept form of the equation is:
\[
y = -4x - 17
\]

The slope is \(-4\) and the y-intercept is \(-17\).

Answer 3

To find a point on the line given by the equation \( y = -4x - 17 \), we can choose any value for \( x \) and calculate the corresponding \( y \) value.

Let’s choose \( x = 0 \) (the y-intercept):

1. Substitute \( x = 0 \) into the equation:
\[
y = -4(0) - 17
\]
\[
y = -17
\]

So the point \( (0, -17) \) is on the line.

You can choose other values for \( x \) as well to find more points on the line. For example, if you choose \( x = 1 \):

2. Substitute \( x = 1 \) into the equation:
\[
y = -4(1) - 17
\]
\[
y = -4 - 17
\]
\[
y = -21
\]

Thus, another point on the line is \( (1, -21) \).

In summary, two points on the line are:
- \( (0, -17) \)
- \( (1, -21) \)