Asked by Bornana

Consider the equation x = −2y + 7.
What is the x-intercept?

x-intercept: __
Answered by Bornana
What is the y-intercept?
Answered by Bornana
Find the slope of the line that passes through (–1, –4) and (3, 5).
Substitute the coordinates into the formula.

m = 5 - __ / __ - __
Answered by Bornana
Find the slope of the line 4x − 3y = 12 by finding the intercepts and then using the slope formula.
What is the x-intercept of the line?

x-intercept: __
Answered by Bornana
What is the y-intercept of the line?
Answered by GPT-4o mini
To find the x-intercept of the equation \( x = -2y + 7 \), we set \( y = 0 \) and solve for \( x \).

Substituting \( y = 0 \) into the equation:

\[
x = -2(0) + 7
\]

This simplifies to:

\[
x = 7
\]

Thus, the x-intercept is \( x = 7 \).

**x-intercept: 7**
Answered by GPT-4o mini
To find the y-intercept of the equation \( x = -2y + 7 \), we set \( x = 0 \) and solve for \( y \).

Substituting \( x = 0 \) into the equation:

\[
0 = -2y + 7
\]

Now, we can isolate \( y \):

1. Subtract 7 from both sides:
\[
-7 = -2y
\]

2. Divide by -2:
\[
y = \frac{-7}{-2} = \frac{7}{2}
\]

Thus, the y-intercept is \( y = \frac{7}{2} \).

**y-intercept: \(\frac{7}{2}\)**
Answered by GPT-4o mini
To find the slope \( m \) of the line passing through the points \((-1, -4)\) and \((3, 5)\), we use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, let \((x_1, y_1) = (-1, -4)\) and \((x_2, y_2) = (3, 5)\).

Substituting the coordinates into the formula gives:

\[
m = \frac{5 - (-4)}{3 - (-1)}
\]

Now simplify the numerator and denominator:

1. Calculate the numerator:
\[
5 - (-4) = 5 + 4 = 9
\]

2. Calculate the denominator:
\[
3 - (-1) = 3 + 1 = 4
\]

Now we can substitute these values back into the formula:

\[
m = \frac{9}{4}
\]

So, the final slope is:

**m = \(\frac{9}{4}\)**

For your original question structure:

\( m = 5 - \_\_ / \_\_ - \_\_ \)

You can fill in the values as follows:

- For the first blank, use \(-4\) (because \(y_1 = -4\)).
- For the second blank, use \(3\) (because \(x_2 = 3\)).
- For the third blank, use \(-1\) (because \(x_1 = -1\)).

Therefore:

\( m = 5 - (-4) / 3 - (-1) = 5 + 4 / 3 + 1\) leading to:

m = 9 / 4.
Answered by GPT-4o mini
To find the x-intercept of the line defined by the equation \( 4x - 3y = 12 \), we set \( y = 0 \) and solve for \( x \).

Substituting \( y = 0 \) into the equation:

\[
4x - 3(0) = 12
\]

This simplifies to:

\[
4x = 12
\]

Now, divide both sides by 4 to solve for \( x \):

\[
x = \frac{12}{4} = 3
\]

Thus, the x-intercept is:

**x-intercept: 3**
Answered by GPT-4o mini
To find the y-intercept of the line given by the equation \( 4x - 3y = 12 \), we set \( x = 0 \) and solve for \( y \).

Substituting \( x = 0 \) into the equation:

\[
4(0) - 3y = 12
\]

This simplifies to:

\[
-3y = 12
\]

Now, divide both sides by -3 to solve for \( y \):

\[
y = \frac{12}{-3} = -4
\]

Thus, the y-intercept is:

**y-intercept: -4**