a line passes through the point (4,6) and has a slope of -5/4. Write an equation in slope-intercept form for this line.

Question

a line passes through the point (4,6) and has a slope of -5/4. Write an equation in slope-intercept form for this line.

Answer 1

y = -(5/4) x + b

6 = -(5/4) * 4 + b
b = 6+5 = 11
so
y = -(5/4) x + 11

Answer 2

Sure, let me put on my mathematical clown nose! 🤡

To find the equation of a line in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we can substitute the given slope (-5/4) and point (4,6) into the formula.

So, let's get started! 🎪

First, let's replace m with -5/4:

y = (-5/4)x + b

Now we'll substitute the coordinates of the point (4,6) into the equation.

6 = (-5/4)(4) + b

Simplifying further, we get:

6 = -5 + b

Now, we'll isolate b by adding 5 to both sides:

6 + 5 = b

11 = b

So, the y-intercept (b) is 11.

Now, we can plug this value back into our equation:

y = (-5/4)x + 11

Viola! There you have it, the equation in slope-intercept form for the line passing through the point (4,6) with a slope of -5/4 is y = (-5/4)x + 11.

🤹‍♂️ Ta-da! Math and humor, all rolled into one!

Answer 3

To write an equation in slope-intercept form for a line, we use the formula:

y = mx + b

Where:
- y and x are the coordinates of a point on the line.
- m is the slope of the line.
- b is the y-intercept of the line.

Given that the line passes through the point (4,6) and has a slope of -5/4, we can substitute these values into the equation:

y = mx + b
6 = (-5/4)(4) + b

Now we solve for b:

6 = (-5/4)(4) + b
6 = -5 + b
b = 6 + 5
b = 11

Now that we have the y-intercept, we can write the equation in slope-intercept form:

y = mx + b
y = (-5/4)x + 11

So, the equation in slope-intercept form for this line is y = (-5/4)x + 11.

Answer 4

To find the equation of a line in slope-intercept form (y = mx + b), we need the slope (m) and a point on the line (x, y). In this case, the given point is (4, 6), and the slope is -5/4.

Step 1: Substitute the values of the point (x, y) into the equation.
y = mx + b
6 = (-5/4)(4) + b

Step 2: Simplify the equation.
6 = -5 + b

Step 3: Isolate the variable (b) by moving -5 to the other side.
6 + 5 = b
11 = b

Step 4: Substitute the value of b back into the equation.
y = (-5/4)x + 11

So, the equation in slope-intercept form for the line passing through the point (4,6) with a slope of -5/4 is y = (-5/4)x + 11.