Question

How can you graph the equation y = 5x + 1| by writing two linear equations? Show both equations, and label the coordinates of the vertex in

your graph.

Answer 1

To graph the equation y = |5x + 1|, split it into y = 5x + 1 when 5x + 1 >= 0, and y = -5x - 1 when 5x + 1 < 0. The vertex is found by setting the inside of the absolute value to zero; it is at the coordinates (-1/5, 0).

Step-by-step explanation:

To graph the equation y = |5x + 1|, we split the equation into two separate linear equations by considering the absolute value. The equation will have two cases depending on whether the expression inside the absolute value is positive or negative.

Case 1: When 5x + 1 ≥ 0, the absolute value has no effect, and the equation is y = 5x + 1.

Case 2: When 5x + 1 < 0, we take the negative of the expression inside the absolute value, making the equation y = -5x - 1.

To find the vertex of the equation y = |5x + 1|, set the inside of the absolute value to zero: 5x + 1 = 0. Solving for x, we get x = -1/5. Substituting that back into the equation yields y = 0.

Thus, the vertex is at the coordinates (-1/5, 0).

Answer 2

To graph the equation y = 5x + 1 by writing two linear equations, plot the y-intercept at (0, 1) and use the slope of 5 to find another point. Connect these points to form the graph.

Step-by-step explanation:

To graph the equation y = 5x + 1 by writing two linear equations, we can break it down into its slope-intercept form, y = mx + b. In this equation, m represents the slope and b represents the y-intercept. The given equation already has the form y = mx + b, with a slope of 5 and a y-intercept of 1.

To graph the equation, we can start by plotting the y-intercept, which is the point (0, 1) on the graph. From there, we can use the slope of 5 to find another point. The slope of 5 means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by 5.

For example, if we increase x by 1, the y-coordinate would increase by 5. So, we can plot another point at (1, 6). Connecting these two points will result in a straight line graph that represents the equation y = 5x + 1.