Find the x and y Intercepts 3x+5y=10

$3 x + 5 y = 10$

Step 1

Find the x-intercepts.

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

$3 x + 5 (0) = 10$

Solve the equation.

Simplify $3 x + 5 (0)$ .

Multiply $5$ by $0$ .

$3 x + 0 = 10$

Add $3 x$ and $0$ .

$3 x = 10$

Divide each term in $3 x = 10$ by $3$ and simplify.

Divide each term in $3 x = 10$ by $3$ .

$\frac{3 x}{3} = \frac{10}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{10}{3}$

Divide $x$ by $1$ .

$x = \frac{10}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{10}{3}, 0)$

Step 2

Find the y-intercepts.

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

$3 (0) + 5 y = 10$

Solve the equation.

Simplify $3 (0) + 5 y$ .

Multiply $3$ by $0$ .

$0 + 5 y = 10$

Add $0$ and $5 y$ .

$5 y = 10$

Divide each term in $5 y = 10$ by $5$ and simplify.

Divide each term in $5 y = 10$ by $5$ .

$\frac{5 y}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10}{5}$

Divide $y$ by $1$ .

$y = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

x-intercept(s): $(\frac{10}{3}, 0)$

y-intercept(s): $(0, 2)$

Step 4

Find the x and y Intercepts 3x+5y=10

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