Question

nd an equation in slope-intercept form for the Fhrough (4,4) and (2,5) The equation of the line is Simplify your answer. Use integers or fractions

Answer 1

To find the equation of a line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope of the line and \( b \) is the y-intercept, we can follow these steps using the two given points (4,4) and (2,5):

Step-by-step explanation:

1. Calculate the slope of the line using the formula:
\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \]
Substitute the coordinates of the two points into the formula:
\[ m = \frac{{5 - 4}}{{2 - 4}} = \frac{{1}}{{-2}} = -\frac{1}{2} \]
So, the slope \( m \) is \( -\frac{1}{2} \).

2. Next, we need to find the y-intercept \( b \). We can do this by substituting one of the points into the slope-intercept form of the equation and solving for \( b \). Let's use the point (4,4):
\[ y = mx + b \]
Substituting the values:
\[ 4 = (-\frac{1}{2})(4) + b \]
Solve for \( b \):
\[ 4 = -2 + b \]
\[ b = 4 + 2 \]
\[ b = 6 \]

Now we have the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = 6 \).

3. Write the equation of the line:
\[ y = -\frac{1}{2}x + 6 \]

This is the equation of the line in slope-intercept form that passes through the points (4,4) and (2,5), simplified using integers and fractions as requested.

Answer 2

The equation of the line in slope-intercept form that passes through points (4,4) and (2,5) is y = -1/2x + 6.

Step-by-step explanation:

The student is looking for the equation of a line in slope-intercept form that passes through points (4,4) and (2,5). To find this, we first calculate the slope (m) of the line using the formula:

m = (y2 – y1) / (x2 – x1)

Substituting the given points into the formula gives us:

m = (5 – 4) / (2 – 4) = 1 / -2 = -1/2

Next, we use the slope and one of the points, say (4,4), to find the y-intercept (b) using the formula:

y – y1 = m(x – x1)

Plugging in the values we have:

4 – 4 = (-1/2)(4 – x1)

This simplifies to b = 4 + 2 = 6. Therefore, the equation of the line in slope-intercept form is:

y = -1/2x + 6