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Question: How can you find the slope and intercept of\[3x - 2y = - 6\]?...

How can you find the slope and intercept of3x2y=63x - 2y = - 6?

Explanation

Solution

Since we need to find the slope and intercept so we need to convert the equation into slope-intercept form by solving yy and any linear equation has the form of y=mx+cy = mx + c where mm stands as slope which can be found by finding two distinct points and cc is the yy intercept where graph hits yy axis.

Formula: Since slope mmdepicts how steep the line is with respect to horizontal. So if in the line two points found are (x1,y1)({x_1},{y_1})and (x2,y2)({x_2},{y_2}) so slope comes out to be
m=y2y1x2x1m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}
The point where line crosses why yy axis is the yy intercept cc

Complete step-by-step solution:
As the given equation is 3x2y=63x - 2y = - 6
Since we know that y=mx+cy = mx + cis the slope intercept form of a line where mm is equal to slope and ccis the yyintercept
Now we will rearrange the given equation into y=mx+cy = mx + c form in order to calculate value of mm and cc
Hence the equation after isolating yy on one side and others on one side

3x2y=6 2y=3x6  \Rightarrow 3x - 2y = - 6 \\\ \Rightarrow - 2y = - 3x - 6 \\\

So we will divide for the coefficient of yywhich is 2 - 2

y=32x+62 y=32x+3  \Rightarrow y = \dfrac{3}{2}x + \dfrac{6}{2} \\\ \Rightarrow y = \dfrac{3}{2}x + 3 \\\

Therefore it means m=32and c = 3m = \dfrac{3}{2}and{\text{ c = 3}}
Now we will plot the graph

Additional Information: Keep in mind that slopes can be negative or positive. Here yywill tell how far a line goes, xx tells us how far along it goes, mm tells about the slope and c is the intercept where the lines crosses yyaxis

Note: While solving the above equation we need to convert the equation given in the slope intercept form and later on after finding the value of mm and cc then pick a point on line and check if it satisfies the equation by plugging it in. So xx intercept is (2,0)( - 2,0) and yy intercept is (0,3)(0,3) which mean line cuts yy
axis at 33