Find the x and y Intercepts (-1,-16) , (0,-15)

$(- 1, - 16)$ , $(0, - 15)$

Step 1

Find the equation using the two points.

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 15 - (- 16)}{0 - (- 1)}$

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $- 16$ .

$m = \frac{- 15 + 16}{0 - (- 1)}$

Add $- 15$ and $16$ .

$m = \frac{1}{0 - (- 1)}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{1}{0 + 1}$

Add $0$ and $1$ .

$m = \frac{1}{1}$

Divide $1$ by $1$ .

$m = 1$

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (1) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (1) \cdot (- 1) + b$

Substitute the value of $y$ into the equation.

$- 16 = (1) \cdot (- 1) + b$

Find the value of $b$ .

Rewrite the equation as $(1) \cdot (- 1) + b = - 16$ .

$(1) \cdot (- 1) + b = - 16$

Multiply $- 1$ by $1$ .

$- 1 + b = - 16$

Move all terms not containing $b$ to the right side of the equation.

Add $1$ to both sides of the equation.

$b = - 16 + 1$

Add $- 16$ and $1$ .

$b = - 15$

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = x - 15$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x - 15$

Solve the equation.

Rewrite the equation as $x - 15 = 0$ .

$x - 15 = 0$

Add $15$ to both sides of the equation.

$x = 15$

x-intercept(s) in point form.

x-intercept(s): $(15, 0)$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (0) - 15$

Solve the equation.

Remove parentheses.

$y = 0 - 15$

Remove parentheses.

$y = (0) - 15$

Subtract $15$ from $0$ .

$y = - 15$

y-intercept(s) in point form.

y-intercept(s): $(0, - 15)$

Step 4

List the intersections.

x-intercept(s): $(15, 0)$

y-intercept(s): $(0, - 15)$

Step 5

Find the x and y Intercepts (-1,-16) , (0,-15)

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