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Consider the equation x = −2y + 7.

What is the x-intercept?

x-intercept: __

9 answers

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

What is the y-intercept?

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: \(\frac{7}{2}\)

Find the slope of the line that passes through (–1, –4) and (3, 5).
Substitute the coordinates into the formula.

m = 5 - __ / __ - __

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.

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: __

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

What is the y-intercept of the line?

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