Question
Question: How can you find the slope and intercept of\[3x - 2y = - 6\]?...
How can you find the slope and intercept of3x−2y=−6?
Solution
Since we need to find the slope and intercept so we need to convert the equation into slope-intercept form by solving y and any linear equation has the form of y=mx+c where m stands as slope which can be found by finding two distinct points and c is the y intercept where graph hits y axis.
Formula: Since slope mdepicts how steep the line is with respect to horizontal. So if in the line two points found are (x1,y1)and (x2,y2) so slope comes out to be
m=x2−x1y2−y1
The point where line crosses why y axis is the y intercept c
Complete step-by-step solution:
As the given equation is 3x−2y=−6
Since we know that y=mx+cis the slope intercept form of a line where m is equal to slope and cis the yintercept
Now we will rearrange the given equation into y=mx+c form in order to calculate value of m and c
Hence the equation after isolating y on one side and others on one side
So we will divide for the coefficient of ywhich is −2
⇒y=23x+26 ⇒y=23x+3Therefore it means m=23and c = 3
Now we will plot the graph
Additional Information: Keep in mind that slopes can be negative or positive. Here ywill tell how far a line goes, x tells us how far along it goes, m tells about the slope and c is the intercept where the lines crosses yaxis
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 m and c then pick a point on line and check if it satisfies the equation by plugging it in. So x intercept is (−2,0) and y intercept is (0,3) which mean line cuts y
axis at 3