Questions: What are the x-intercept and y-intercept of the line y=4x+58? a) x-intercept (4,0) y-intercept (0, 4/5) b) x intercept: (-5/4, 0) y-intercept: (0,5) c) x-intercept (5,0) y-intercept (0,-5/4)

What are the x-intercept and y-intercept of the line y=4x+58? a) x-intercept (4,0) y-intercept (0, 4/5) b) x intercept: (-5/4, 0) y-intercept: (0,5) c) x-intercept (5,0) y-intercept (0,-5/4)
Transcript text: What are the x-intercept and y-intercept of the line $y=4 x+58$ a) x-intercept $(4,0)$ y-intercept $\left(0, \frac{4}{5}\right)$ b) $x$ intercept: $\left(-\frac{5}{4}, 0\right)$ $y$-intercept: $(0,5)$ c) $x$-intercept $(5,0)$ y-intercept $\left(0,-\frac{5}{4}\right)$
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Solution

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Solution Steps

To find the x-intercept and y-intercept of the line given by the equation \( y = 4x + 58 \):

  1. X-intercept: Set \( y = 0 \) and solve for \( x \).
  2. Y-intercept: Set \( x = 0 \) and solve for \( y \).
Step 1: Finding the X-Intercept

To find the x-intercept, we set \( y = 0 \) in the equation \( y = 4x + 58 \):

\[ 0 = 4x + 58 \]

Solving for \( x \):

\[ 4x = -58 \implies x = -\frac{58}{4} = -14.5 \]

Thus, the x-intercept is \( (-14.5, 0) \).

Step 2: Finding the Y-Intercept

To find the y-intercept, we set \( x = 0 \) in the equation \( y = 4x + 58 \):

\[ y = 4(0) + 58 = 58 \]

Thus, the y-intercept is \( (0, 58) \).

Final Answer

The x-intercept is \( (-14.5, 0) \) and the y-intercept is \( (0, 58) \).

\[ \boxed{\text{x-intercept: } (-14.5, 0), \text{ y-intercept: } (0, 58)} \]

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