Question

Question in pic (50 points!)

Answer 1

Slope-intercept form

• y = (-5/4)x + 5

Explanation:

The coordinates are,

→ x1 = 0, y1 = 5

→ x2 = 4, y2 = 0

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (0 - 5)/(4 - 0)

→ [ m = -5/4 ]

The y-intercept is,

→ y1 = 5

→ [ b = 5 ]

Then slope-intercept form is,

→ y = mx + b

→ y = (-5/4)x + 5

Thus, answer is y = (-5/4)x + 5.

Answer 2

`y=-(5)/(4)x+5`

Explanation:

`\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}`

From inspection of the given graph, two points on the line are:

• A = (0, 5)
• B = (4, 0)

Substitute the two points into the slope formula to find the slope of the line:

`\implies m=(0-5)/(4-0)=-(5)/(4)`

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

From inspection of the given graph, the y-intercept is (0, 5), therefore b = 5. Substitute the found slope and y-intercept into the slope-intercept formula:

`\implies y=-(5)/(4)x+5`