Questions: Find the x and y intercepts of the equation: y=7x+4

Find the x and y intercepts of the equation: y=7x+4
Transcript text: Find the $x$ and $y$ intercepts of the equation: $y=7 x+4$
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Solution

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Solution Steps

Step 1: Find the \( x \)-intercept

To find the \( x \)-intercept, set \( y = 0 \) in the equation \( y = 7x + 4 \) and solve for \( x \): \[ 0 = 7x + 4 \] \[ 7x = -4 \] \[ x = -\frac{4}{7} \] The \( x \)-intercept is \( \left( -\frac{4}{7}, 0 \right) \).

Step 2: Find the \( y \)-intercept

To find the \( y \)-intercept, set \( x = 0 \) in the equation \( y = 7x + 4 \) and solve for \( y \): \[ y = 7(0) + 4 \] \[ y = 4 \] The \( y \)-intercept is \( (0, 4) \).

Step 3: Write the intercepts in the required format

The intercepts are: \[ x \text{ intercept } = \left( -\frac{4}{7}, 0 \right) \] \[ y \text{ intercept } = (0, 4) \]

Final Answer

The \( x \) intercept is \( \boxed{\left( -\frac{4}{7}, 0 \right)} \) and the \( y \) intercept is \( \boxed{(0, 4)} \).

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