Linear Functions Practice Problems y=mx+b - Slope & Y-Intercept

In the exercise, we have an inequality equation.

We treat the inequality as an equation with the sign -=,

And we only refer to it if we need to multiply or divide by 0.

 $10x-4 ≤ -3x-8$

We start by organizing the sections:

$10x+3x-4 ≤ -8$

$13x-4 ≤ -8$

$13x ≤ -4$

Divide by 13 to isolate the X

$x≤-\frac{4}{13}$

Let's look again at the options we were asked about:

Answer A is with different data and therefore was rejected.

Answer C shows a case where X is greater than$-\frac{4}{13}$, although we know it is small, so it is rejected.

Answer D shows a case (according to the white circle) where X is not equal to$-\frac{4}{13}$, and only smaller than it. We know it must be large and equal, so this answer is rejected.

Therefore, answer B is the correct one!

To solve this problem, we need to determine the slope of the line depicted on the graph.

First, understand that the slope of a line on a coordinate plane indicates how steep the line is and the direction it is heading. Specifically:

• A positive slope means the line rises as it goes from left to right.
• A negative slope means the line falls as it goes from left to right.

Let's examine the graph given:

• We see that the line starts at a higher point on the left and descends to a lower point on the right side.
• As we move from the left side of the graph towards the right, the line goes downwards.

This downward trajectory clearly indicates a negative slope because the line is declining as we move horizontally left to right.

Therefore, the slope of this function is Negative.

The correct answer is, therefore, Negative slope.

To solve this problem, let's analyze the given graph of the function to determine the slope's sign.

The slope of a line on a graph indicates the line's direction. A line with a positive slope rises as it moves from left to right, indicating that for every step taken to the right (along the x-axis), we move upward. Conversely, a line with a negative slope falls as it moves from left to right, meaning each step to the right results in moving downward.

Examining the graph provided, the red line starts higher on the left and goes downward towards the right visually. This indicates that the line is rising as it goes from left to right, which confirms it has a positive slope.

Therefore, the solution to the problem, regarding the slope of the line, is that it is a Positive slope.

To solve this problem, let's evaluate the graph of the line provided:

• The line is visually represented as starting from the bottom left to the top right, moving upwards.
• In a standard Cartesian graph, a line that ascends as it progresses from left to right implies a positive change in the y-coordinate as the x-coordinate increases.
• This upward trajectory indicates that the slope, $m$, is positive.

Thus, the slope of the function is positive.

Therefore, the answer is Positive slope.

To determine the slope of the line, we'll examine the direction of the line segment on the graph:

• The line depicted moves from the top left, passing through a point with higher $y$-coordinate values, to the bottom right, ending at a point with lower $y$-coordinate values.
• This movement indicates that as $x$ increases (the direction to the right along the $x$-axis), the $y$-coordinate decreases.
• When the $y$-value reduces as the $x$-value grows, the slope $m$ is negative.

Since the line descends from left to right, the slope of the line is negative.

Therefore, the slope of the function is a negative slope.