find the slope of the line given by each equation
(1) 7x+13y=91
(2) 7-3y=9x
to find the slope of the line, we transform this given equation in the form,
y = mx + b
where m = slope and b = y-intercept
thus for (1) 7x + 13y = 91, we first divide all term by numerical coefficient of y (which is 13) to get y alone:
(7/13)x + (13/13)y = 91/13
(7/13)x + y = 7
now, to have this in the form y = mx + b, we transpose (7/13)x to the other side of equation,, to do this we change its sign from positive to negative:
y = 7 - (7/13)x or
y = -(7/13)x + 7
thus m = slope = -(7/13)
for (b), we do the same thing:
7 - 3y = 9x
we transpose 7 to other side, changing its sign from positive to negative:
-3y = 9x - 7
then we divide all terms by -3 to get y alone:
y = 9/(-3) x - 7/(-3)
y = -3x + (7/3)
thus m = slope = -3
hope this helps~ :)
To find the slope of a line given by an equation in the form Ax + By = C, we need to rearrange the equation into slope-intercept form, which has the form y = mx + b. Once we have the equation in this form, we can read off the slope, m, directly.
Let's find the slope for each equation:
(1) 7x + 13y = 91
To rearrange this equation into slope-intercept form, we need to isolate y on one side of the equation.
First, subtract 7x from both sides:
13y = -7x + 91
Next, divide both sides by 13 to solve for y:
y = (-7/13)x + (91/13)
Now we can see that the equation is in slope-intercept form, and the slope of the line is -7/13.
(2) 7 - 3y = 9x
To rearrange this equation into slope-intercept form, we need to isolate y on one side of the equation.
First, subtract 7 from both sides:
-3y = 9x - 7
Next, divide both sides by -3 to solve for y:
y = (-9/3)x + (7/3)
Simplifying the expression further, we have:
y = -3x + (7/3)
Now we can see that the equation is in slope-intercept form, and the slope of the line is -3.