Answer:
y= 2x -6
Step-by-step explanation:
The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
To find the equation of a line, two information are needed:
Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:
y= 2x +c
Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.
2x -3y= 6
When x= 3,
2(3) -3y= 6
6- 3y= 6
3y= 6 -6
3y= 0
Divide both sides by 3:
y= 0
Coordinate that lies on the graph is (3, 0).
Substitute the point into the equation and solve for c:
y= 2x +c
When x= 3, y= 0,
0= 2(3) +c
0= 6 +c
c= -6
Substitute the value of c back into the equation:
Thus, the equation of the line in slope-intercept form is y= 2x -6.
Additional:
For a similar question on slope-intercept form, do check out the following!
