Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The equation
is a straight line with a slope of
and a y-intercept at (0, -4). It crosses the x-axis at (12, 0).
Solución
Certainly! Let’s analyze the linear equation you’ve provided:
This equation is in slope-intercept form, which is generally written as:
where:
-
is the slope of the line. -
is the y-intercept, the point where the line crosses the y-axis.
Breakdown of the Equation
-
Slope (
): - In your equation,
. - Interpretation: For every increase of 3 units in
, increases by 1 unit. - Graphically: The line rises gently from left to right.
- In your equation,
-
Y-Intercept (
): - Here,
. - Interpretation: The line crosses the y-axis at the point (0, -4).
- Graphically: Start your graph at the point (0, -4).
- Here,
Graphing the Equation
To graph the equation
:
-
Plot the Y-Intercept:
- Start by plotting the y-intercept at (0, -4).
-
Use the Slope to Find Another Point:
- The slope
means “rise over run.” So, for every 3 units you move horizontally (run) to the right, you move 1 unit vertically (rise) upwards. - Starting from (0, -4), move 3 units to the right to
, and 1 unit up to . Plot the point (3, -3).
- The slope
-
Draw the Line:
- Connect the two points with a straight line extending in both directions.
Additional Features
-
X-Intercept:
-
To find where the line crosses the x-axis, set
and solve for : -
So, the x-intercept is at (12, 0).
-
-
Increasing/Decreasing:
- Since the slope
is positive, the line is increasing; as increases, also increases.
- Since the slope
Summary
- Slope:
(gentle upward incline) - Y-Intercept: (0, -4)
- X-Intercept: (12, 0)
- Graph: A straight line crossing the y-axis at (0, -4) and the x-axis at (12, 0), rising as it moves from left to right.
If you have any specific questions about this equation or need further assistance, feel free to ask!
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
Did you know that the equation you provided,
, represents a straight line on a graph? The slope of
indicates that for every 3 units you move to the right along the x-axis, you’ll move up 1 unit on the y-axis. This slope is gentle, giving the line a nice, gradual incline!
Now, if you’re looking to find the x-intercept of this line, you can set
to 0 and solve for
. Setting
leads to
. This means the line crosses the x-axis at (12, 0). A great way to visualize graphing this line is to plot these points and connect them—it’ll help reinforce your understanding of linear equations!
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