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2 years ago

write the equation of the line that passes through the given points expressed in slope-intercept form. m=2/3, (-4,5)

Mathematics

1 answer:

solniwko [45]2 years ago

7 0

Answer:

$y = \frac{2}{3}x + \frac{23}{3}$

Step-by-step explanation:

To write the equation of a line with a point and a slope, use the point-slope form of a linear equation. Substitute m = 2/3 and the point (-4,5) into the equation.

$y - y_1 = m(x-x_1)\\y - 5 = \frac{2}{3}(x --4)\\y - 5 = \frac{2}{3}(x+4)$

Convert to slope intercept form by using the distributive property.

$y - 5 = \frac{2}{3}(x+4)\\y - 5 = \frac{2}{3}x +\frac{8}{3}\\y = \frac{2}{3}x + \frac{8}{3} + 5\\y = \frac{2}{3}x + \frac{23}{3}$

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maks197457 [2]

Answer:

1) 20 stars; 30 points.

2) 28 stars, 42 points.

3) 38 stars, 57 points.

Step-by-step explanation:

<h3> The missing table is attached.</h3>

Let be "x" the numbers of stars Roberto collects and "y" his total points.

The proportional relationship has this form:

$y=kx$

Where "k" is the constant of proportionality.

We can choose the point $(8,12$ ) from the table, where:

$x=8\\y=12$

Substituting these values into $y=kx$ and solving for "k", we get:

$12=k(8)\\\\\frac{12}{8}=k\\\\k=1.5$

Knowing the value of "k", we determine that the following Numbers of stars and the Total points could be used as the missing values in the table:

1) For $x=20$ :

$y=(1.5)(20)=30$

2) For $x=28$ :

$y=(1.5)(28)=42$

3) For $x=38$ :

$y=(1.5)(38)=57$

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