\begin{tabular}{l|l} Finding & $$ \begin{array}{l} ext { To find the } x ext {-intercept of an equation, set } y ext { equal to } 0 ext { and solve for } x \ ext { To find the } y ext {-intercept of an equation, set } x ext { equal to } 0 ext { and solve for } y \ ext { You can use these points to graph the equation. } \ ext { cepts }\end{array} $$ \ $$ \begin{array}{l} ext { Example: Find the } x ext {-and } y ext {-intercepts of the equation } y=-2 x+5\end{array} $$ \ & \end{tabular}

Question

\begin{tabular}{l|l} Finding & $$ \begin{array}{l}	ext { To find the } x 	ext {-intercept of an equation, set } y 	ext { equal to } 0 	ext { and solve for } x \ 	ext { To find the } y 	ext {-intercept of an equation, set } x 	ext { equal to } 0 	ext { and solve for } y \ 	ext { You can use these points to graph the equation. } \ 	ext { cepts }\end{array} $$ \ $$ \begin{array}{l}	ext { Example: Find the } x 	ext {-and } y 	ext {-intercepts of the equation } y=-2 x+5\end{array} $$ \ & \end{tabular}

UpStudy AI · Accepted Answer

To find the $$ x $$-intercept and $$ y $$-intercept of the equation $$ y = -2x + 5 $$, we will follow the steps outlined in your table.

### Step 1: Finding the $$ x $$-intercept
To find the $$ x $$-intercept, we set $$ y = 0 $$ and solve for $$ x $$.

$$
0 = -2x + 5
$$

Now, we will solve for $$ x $$:

$$
-2x = -5
$$

Dividing both sides by $$-2$$:

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

Thus, the $$ x $$-intercept is $$ \left( \frac{5}{2}, 0 \right) $$.

### Step 2: Finding the $$ y $$-intercept
To find the $$ y $$-intercept, we set $$ x = 0 $$ and solve for $$ y $$.

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

This simplifies to:

$$
y = 5
$$

Thus, the $$ y $$-intercept is $$ (0, 5) $$.

### Summary of Intercepts
- The $$ x $$-intercept is $$ \left( \frac{5}{2}, 0 \right) $$.
- The $$ y $$-intercept is $$ (0, 5) $$.

These points can be used to graph the equation $$ y = -2x + 5 $$.
To find the $$ x $$-intercept, set $$ y = 0 $$ and solve for $$ x $$. For $$ y = -2x + 5 $$, this gives $$ x = \frac{5}{2} $$, so the $$ x $$-intercept is $$ \left( \frac{5}{2}, 0 \right) $$. To find the $$ y $$-intercept, set $$ x = 0 $$ and solve for $$ y $$. For $$ y = -2x + 5 $$, this gives $$ y = 5 $$, so the $$ y $$-intercept is $$ (0, 5) $$. These intercepts help in graphing the equation.

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