for what value of k does kx + 7y = 10 have a slope of 3? im really confused!!!
Rewrite the equation in the form
y = -(k/7)x + 10/7
You want the slope (-k/7) to be 3
-k/7 = 3
k = ?
-k/7=3
-k=21
k=-21
To find the value of k that makes the equation kx + 7y = 10 have a slope of 3, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope. Here's how you can do it step-by-step:
Step 1: Start with the given equation: kx + 7y = 10.
Step 2: Rearrange the equation to isolate y:
7y = -kx + 10.
Step 3: Divide all terms by 7 to get y by itself:
y = (-k/7)x + 10/7.
Now we can see that the slope of the equation is -k/7.
Step 4: Set the slope equal to 3 and solve for k:
- k/7 = 3.
Step 5: Multiply both sides of the equation by 7 to get rid of the fraction:
- k = 21.
Step 6: Finally, multiply both sides of the equation by -1 to solve for k:
k = -21.
So, when k is equal to -21, the equation kx + 7y = 10 has a slope of 3.
To find the value of k that gives the equation a slope of 3, we need to recognize that the standard form of a linear equation can be written as y = mx + b, where m is the slope of the line. In this case, the equation is given as kx + 7y = 10.
To determine the slope of the line given by this equation, we need to rewrite it in the form y = mx + b. Let's isolate the y variable by subtracting kx from both sides:
7y = -kx + 10
Now, divide both sides of the equation by 7 to solve for y:
y = (-k/7)x + (10/7)
Comparing this to the standard form, we can see that the slope, which is the coefficient of x, is equal to -k/7. We want this slope to be 3. So we can set up an equation:
- (k/7) = 3
To solve for k, we can multiply both sides of the equation by 7 to get rid of the fraction:
- k = 3 * 7
Simplifying the right side of the equation, we have:
- k = 21
Now, multiply both sides of the equation by -1 to solve for k:
k = -21
Therefore, for the equation kx + 7y = 10 to have a slope of 3, the value of k should be -21.