Question

What is the slope-intercept equation for the linear function represented by the

table?
X 0 2 4 6 8
y -7 -2 3 8 13
A. y = 2/5x + 7
B. y = 2/5x - 7
C. y = 5/2x - 7
D. y = 5/2x + 7
​

Answer 1

Answer:
`\( \text{C. } y = (5)/(2)x - 7 \).`

Explanation:

To find the slope-intercept equation of the linear function represented by the table, we need to determine two things:

1. The slope
`(\( m \))` of the line

2. The y-intercept
`(\( b \))`

Step 1: Finding the Slope

The slope
`(\( m \))` is calculated as the change in \( y \) divided by the change in
`\( x \)`:

`\[m = \frac{{\Delta y}}{{\Delta x}}\]`

We can pick any two points from the table to calculate the slope. Let's use the points
`\( (0, -7) \)` and
`\( (2, -2) \)`:

`\[m = \frac{{-2 - (-7)}}{{2 - 0}} = \frac{{5}}{2}\]`

Step 2: Finding the y-intercept

The y-intercept
`(\( b \))` is the value of
`\( y \)`when
`\( x = 0 \)`. According to the table, when
`\( x = 0 \), \( y = -7 \)`.

Step 3: Writing the Equation

The slope-intercept form of a linear equation is
`\( y = mx + b \)`.

Substituting the values we found for
`\( m \)` and
`\( b \)`, we get:

`\[y = (5)/(2)x - 7\]`

So, the correct answer is
`\( \text{C. } y = (5)/(2)x - 7 \)`.

Answer 2

C

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (8, 13) ← 2 ordered pairs from the table

substitute these values into the formula for m

m =
`(13-(-2))/(8-2)` =
`(13+2)/(6)` =
`(15)/(6)` =
`(5)/(2)`

the line crosses the y- axis at (0, - 7 ) , then y- intercept c = - 7

y =
`(5)/(2)` x - 7 ← equation of line