Which graph represents the equation y=13x−4?

Question

A. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair negative 2 comma 1 end ordered pair.

B. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair 3 comma negative 3 end ordered pair.

C. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair negative 4 comma 0 end ordered pair and begin ordered pair negative 3 comma 3 end ordered pair.

D. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair negative 4 comma 0 end ordered pair and begin ordered pair 3 comma negative 3 end ordered pair.

Answer 1

To determine which graph represents the equation \( y = 13x - 4 \), we can analyze the slope and y-intercept from the equation.

1. Identify the slope and y-intercept: The equation \( y = 13x - 4 \) is in slope-intercept form \( y = mx + b \), where:

   • \( m \) (slope) = 13
   • \( b \) (y-intercept) = -4

2. Y-Intercept: The y-intercept means that when \( x = 0 \), \( y = -4 \). Therefore, one point on the line is \( (0, -4) \).

3. Finding another point: The slope of 13 indicates that for every 1 unit you move to the right (in the x-direction), you move up 13 units (in the y-direction). We can choose \( x = 1 \):

   • If \( x = 1 \): \[ y = 13(1) - 4 = 13 - 4 = 9 \]
   • Therefore, another point on the line is \( (1, 9) \).

Let's check which of the provided options contains the points \( (0, -4) \) and another point consistent with the slope of 13 or is related to those points:

• Option A: Includes the points \( (0, -4) \) and \( (-2, 1) \). This does not fit as \( (-2, 1) \) does not correspond to the line based on the steep slope of 13.

• Option B: Includes \( (0, -4) \) and \( (3, -3) \). Here, \( (3, -3) \) does not align with the expected direction or steepness of the line.

• Option C: Includes the points \( (-4, 0) \) and \( (-3, 3) \). This also does not match our line.

• Option D: Includes \( (-4, 0) \) and \( (3, -3) \). Similar to the previous options, this does not fit with the line we established from the equation.

None of the graphs provided match the line defined by the equation \( y = 13x - 4 \) properly, as they don't propose points reflecting the rapid growth in \( y \) relative to \( x \).

So, the correct line representation should have points that reflect a very steep slope, like those iterating the pattern established above. Unfortunately, based on the choices given, none correctly meet the characteristics determined from \( y = 13x - 4 \). If you have further options or a clarifying statement about the graphs, it might yield a more accurate identification.