Problem 28 list (a) the coordinates of any ... [FREE SOLUTION]

Chapter 3: Problem 28

list (a) the coordinates of any $y$ -intercept and (b) the coordinates of any $x$ -intercept. Do not graph. $$ 4 x-3 y=24 $$

Short Answer

Expert verified

The y-intercept is (0, -8) and the x-intercept is (6, 0).

Step by step solution

Identify the coordinates of the y-intercept

To find the y-intercept, set $x = 0$ in the equation. Substitute $x = 0$ into the equation: \[4(0) - 3y = 24\] Simplify to find $y$: \[-3y = 24\] Divide by -3: \[y = -8\] So, the coordinates of the y-intercept are $(0, -8)$.

Identify the coordinates of the x-intercept

To find the x-intercept, set $y = 0$ in the equation. Substitute $y = 0$ into the equation: \[4x - 0 = 24\] Simplify to find $x$: \[4x = 24\] Divide by 4: \[x = 6\] So, the coordinates of the x-intercept are $(6, 0)$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

y-intercept

The y-intercept is where a graph crosses the y-axis. At this point, the value of x is always 0 because the y-axis is where all the x-coordinates are zero. To find the y-intercept of a linear equation, you set x to 0 and solve for y. In the given equation, $4x - 3y = 24$, setting $x = 0$ gives us $4(0) - 3y = 24$. Simplifying this, we get $-3y = 24$, and dividing by $-3$ results in $y = -8$. Therefore, the y-intercept is at $(0, -8)$.

This means if you were to plot this on a graph, the point where the line crosses the y-axis would be at -8.

x-intercept

The x-intercept is where a graph crosses the x-axis. At this point, the value of y is always 0 because the x-axis is where all the y-coordinates are zero. To find the x-intercept of a linear equation, you set y to 0 and solve for x. In the given equation, $4x - 3y = 24$, setting $y = 0$ gives us $4x - 0 = 24$. Simplifying this, we get $4x = 24$, and dividing by $4$ results in $x = 6$. Therefore, the x-intercept is at $(6, 0)$.

This means if you were to plot this on a graph, the point where the line crosses the x-axis would be at 6.

linear equations

Linear equations are algebraic expressions that represent straight lines on a graph. They are typically written in the form $Ax + By = C$ where A, B, and C are constants. The graph of a linear equation is a straight line because it shows a constant rate of change. The coefficients of x and y (A and B) dictate the slope of the line, while C affects its position.

Finding intercepts helps understand the equation's graph. The y-intercept gives the point where the line meets the y-axis, and the x-intercept shows where it meets the x-axis. By determining these points, you can graph the line easily even if you don't know its slope.

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91影视

list (a) the coordinates of any \(y\) -intercept and (b) the coordinates of any \(x\) -intercept. Do not graph. $$ 4 x-3 y=24 $$

Short Answer

Step by step solution

Identify the coordinates of the y-intercept

Identify the coordinates of the x-intercept

Key Concepts

y-intercept

x-intercept

linear equations

One App. One Place for Learning.

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