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Question: How do you find the slope and intercept to graph \(3x + 4y = - 12\) ?...

How do you find the slope and intercept to graph 3x+4y=−123x + 4y = - 12 ?

Explanation

Solution

The equation of a straight line in slope-intercept form is: y=mx+by = mx + b. Where m is the value of slope and b is the y-intercept. Here, m and b are constants, and x and y are variables. Since x and y are variables that describe the position of specific points on the graph, m and b describe features of the function. In this question, a linear equation is given. We will convert this equation into the form of a straight-line equation. By comparing with the standard equation we will find the value of slope and the value of intercept.

Complete step-by-step answer:
In this question, the linear equation is
⇒3x+4y=−12\Rightarrow 3x + 4y = - 12
Let us subtract 3x both sides.
⇒3x−3x+4y=−12−3x\Rightarrow 3x - 3x + 4y = - 12 - 3x
Therefore,
⇒4y=−12−3x\Rightarrow 4y = - 12 - 3x
Now, let us divide both sides by 4.
⇒y=−12−3x4\Rightarrow y = \dfrac{{ - 12 - 3x}}{4}
Let us split the denominator.
⇒y=−3x4−124\Rightarrow y = \dfrac{{ - 3x}}{4} - \dfrac{{12}}{4}
Hence,
⇒y=−3x4−3\Rightarrow y = \dfrac{{ - 3x}}{4} - 3
Now, compare the above equation with a straight line equationy=mx+by = mx + b
So, we get m=−34m = \dfrac{{ - 3}}{4}andb=−3b = - 3

Hence, the value of slope is −34\dfrac{{ - 3}}{4} and the value of intercept is -3.

Note:
Slope: The slope of a line is defined as the ratio of change in y over the change in x between any two points on the line.
slope(m)=y2−y1x2−x1slope\left( m \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}
Positive slope: It means that two variables are positively related; that is, when x increases, so do y, and when x decreases, y decreases also. The line with the positive slope on the line graph moves from left to right and the line rises.
Negative slope: A negative slope means that two variables are negatively related; that is, when x increases, y decreases, and when x decreases, y increases. The line with the negative slope on the line graph moves from left to right and the line falls.
The slope is a horizontal line then the value of y is always the same.
The slope is a vertical line then the value of x is always the same.