Find the slope and the y-intercept of the line which has the equation 2x + 3y = 9.
The slope-intercept equation of a line is y = mx+c, where m is the slope of the line and c is the y-intercept.
Answer: The slope and the y-intercept of the line which has the equation 2x + 3y = 9 are - 2 / 3 and 3, respectively.
Let us see how we will use the concept of straight lines in order to find the slope and y-intercept.
In order to deal with the equation, we will first convert the equation 2x + 3y = 9 in slope-intercept form, that is, y = mx + c.
In the equation y = mx + c, m is the slope, and c is the y-intercept.
Subtract 2x from both the sides of the equation 2x + 3y = 9.
2x + 3y - 2x = 9 -2x
3y = 9 - 2x
Divide the whole equation 3y = 9 - 2x by 3. On performing this transformation, we get y = (-2 / 3) x + 3.
On comparing with the general form of the slope-intercept equation, we have m = -2/3 and c = 3
Hence, on comparing with y = mx + c, we get m (slope) = (-2 / 3) and c (y-intercept) = 3