what is the equation, in slope- intercept form, of the line that contains the points (-3,4) and (5,7)

Mathematics

1 answer:

gavmur [86]3 years ago

6 0

Answer:

y = $\frac{3}{8}$ x + $\frac{41}{8}$

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

To calculate the slope use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (5, 7)

m = $\frac{7-4}{5+3}$ = $\frac{3}{8}$ , hence

y = $\frac{3}{8}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

using (5, 7 ), then

7 = $\frac{15}{8}$ + c ⇒ c = 7 - $\frac{15}{8}$ = $\frac{41}{8}$

y = $\frac{3}{8}$ x + $\frac{41}{8}$ ← equation in slope-intercept form

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Step-by-step explanation:

1) Below there are the missing data:

A proportional relationship through a constant k. It is obtained when we divide:

$k=\frac{y}{x}$

2)In this case, when we divide the temperature (T) by the time (h).

$k=\frac{T}{h}$

3)So, examining the table below we are searching for a ratio k common to all measures (temperatures over hour).

$A) \frac{12}{3}\neq\frac{25}{5}\neq\frac{36}{6}\neq\frac{81}{9}\\B) \frac{22.5}{3}\neq\frac{30}{4}\neq\frac{52.5}{7}\neq\frac{67.5}{8}\\C)\frac{10}{2}=\frac{15}{3}=\frac{25}{5}=\frac{40}{8}=k= 5\\D)\frac{8.5}{2}\neq\frac{22.5}{5}\neq\frac{28.5}{7}\neq\frac{36}{8}$