Find the x and y Intercepts y-3=5(x-2)

$y - 3 = 5 (x - 2)$

Step 1

Find the x-intercepts.

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

$(0) - 3 = 5 (x - 2)$

Solve the equation.

Rewrite the equation as $5 (x - 2) = (0) - 3$ .

$5 (x - 2) = (0) - 3$

Subtract $3$ from $0$ .

$5 (x - 2) = - 3$

Divide each term in $5 (x - 2) = - 3$ by $5$ and simplify.

Divide each term in $5 (x - 2) = - 3$ by $5$ .

$\frac{5 (x - 2)}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (x - 2)}{5} = \frac{- 3}{5}$

Divide $x - 2$ by $1$ .

$x - 2 = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x - 2 = - \frac{3}{5}$

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

Add $2$ to both sides of the equation.

$x = - \frac{3}{5} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - \frac{3}{5} + 2 \cdot \frac{5}{5}$

Combine $2$ and $\frac{5}{5}$ .

$x = - \frac{3}{5} + \frac{2 \cdot 5}{5}$

Combine the numerators over the common denominator.

$x = \frac{- 3 + 2 \cdot 5}{5}$

Simplify the numerator.

Multiply $2$ by $5$ .

$x = \frac{- 3 + 10}{5}$

Add $- 3$ and $10$ .

$x = \frac{7}{5}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{7}{5}, 0)$

Step 2

Find the y-intercepts.

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

$y - 3 = 5 ((0) - 2)$

Solve the equation.

Simplify $5 ((0) - 2)$ .

Subtract $2$ from $0$ .

$y - 3 = 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$y - 3 = - 10$

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

Add $3$ to both sides of the equation.

$y = - 10 + 3$

Add $- 10$ and $3$ .

$y = - 7$

y-intercept(s) in point form.

y-intercept(s): $(0, - 7)$

Step 3

List the intersections.

x-intercept(s): $(\frac{7}{5}, 0)$

y-intercept(s): $(0, - 7)$

Step 4

Find the x and y Intercepts y-3=5(x-2)

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