Find the x and y Intercepts y+17=3(x+6)-14

$y + 17 = 3 (x + 6) - 14$

Step 1

Find the x-intercepts.

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

$(0) + 17 = 3 (x + 6) - 14$

Solve the equation.

Rewrite the equation as $3 (x + 6) - 14 = (0) + 17$ .

$3 (x + 6) - 14 = (0) + 17$

Simplify $3 (x + 6) - 14$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 6 - 14 = (0) + 17$

Multiply $3$ by $6$ .

$3 x + 18 - 14 = (0) + 17$

Subtract $14$ from $18$ .

$3 x + 4 = (0) + 17$

Add $0$ and $17$ .

$3 x + 4 = 17$

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

Subtract $4$ from both sides of the equation.

$3 x = 17 - 4$

Subtract $4$ from $17$ .

$3 x = 13$

Divide each term in $3 x = 13$ by $3$ and simplify.

Divide each term in $3 x = 13$ by $3$ .

$\frac{3 x}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{13}{3}$

Divide $x$ by $1$ .

$x = \frac{13}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{13}{3}, 0)$

Step 2

Find the y-intercepts.

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

$y + 17 = 3 ((0) + 6) - 14$

Solve the equation.

Simplify $3 ((0) + 6) - 14$ .

Simplify each term.

Add $0$ and $6$ .

$y + 17 = 3 \cdot 6 - 14$

Multiply $3$ by $6$ .

$y + 17 = 18 - 14$

Subtract $14$ from $18$ .

$y + 17 = 4$

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

Subtract $17$ from both sides of the equation.

$y = 4 - 17$

Subtract $17$ from $4$ .

$y = - 13$

y-intercept(s) in point form.

y-intercept(s): $(0, - 13)$

Step 3

List the intersections.

x-intercept(s): $(\frac{13}{3}, 0)$

y-intercept(s): $(0, - 13)$

Step 4

Find the x and y Intercepts y+17=3(x+6)-14

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