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3 years ago

The equation shows the relationship between x and y:

Mathematics

2 answers:

miss Akunina [59]3 years ago

8 0

Okay so your slope is going to be -9 because that is the rise over run for that equation. 5 is you y-intercept.

AVprozaik [17]3 years ago

6 0

Answer:

The correct option is 2. The slope of the equation is -9.

Step-by-step explanation:

The given equation is

$y=-9x+5$ ..... (1)

The slope intercept form of a line is

$y=mx+b$ .... (2)

Where, m is the slope and b is y-intercept.

On comparing (1) and (2), we get

$m=-9$

and

$b=5$

Therefore, the slope of the equation is -9 and y-intercept is (0,5). Option 2 is correct.

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4 years ago

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3 years ago

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4 years ago

The line on the graph passes through to points A (1, 3) B (7, 1)

Flura [38]

Answer:

a. Gradient of line AB is $-\frac{1}{3}$

b. The gradient of a line perpendicular to line AB is 3

c. The equation of a line passing through point (4,2) and perpendicular to AB is $y = 3x - 10$

Step-by-step explanation:

Given

Point A (1, 3) B (7, 1)

Required

Gradient of AB

Gradient of a line is represented by m

m is calculated using the following formula

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

Where the general representation of the coordinates are $A(x_1,y_1) and B(x_2,y_2)$

From the given data, we have that

$A(x_1,y_1) = A(1,3)$

$B(x_2,y_2) = A(7,1)$

So, from there we know that

$x_1 = 1;y_1 =3; x_2 = 7;y_2 =1$

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$ becomes

$m = \frac{1 - 3}{7 - 1}$

$m = \frac{-2}{6}$

$m = -\frac{1}{3}$

Required

Find the gradient of a line perpendicular to AB

Recall that gradient of a line is represented by m

The condition for perpendicularity is that $m_1.m_2 = -1$

In (a) above, we solved the gradient of line AB to be $-\frac{1}{3}$

Let $m_1$ represent gradient of line AB

Hence, $m_1 = -\frac{1}{3}$

Substitute $-\frac{1}{3}$ for $m_1$ in $m_1.m_2 = -1$

This will give

$\frac{-1}{3} * m_2 = -1$

Multiply both sides by -3

$-3 * \frac{-1}{3} * m_2 = -1 * -3$

$m_2 = -1 * -3$

$m_2 = 3$

Hence, the gradient of a line perpendicular to line AB is 3

Required

Find the equation of a line passing through point (4,2) and perpendicular to AB

Equation is calculated using the gradient formula

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

Since only one point is known, the formula is represented as follows

$m = \frac{y - y_{1} }{x - x_{1}}$

Where $x_1 = 4; y_1 = 2$

Since, the line is perpendicular to line AB, then its gradient m is equal to 3 (as calculated in b above)

So, we have $x_1 = 4; y_1 = 2; m = 3$

By substitution

$m = \frac{y - y_{1} }{x - x_{1}}$ becomes

$3 = \frac{y - 2}{x - 4}$

Multiply both sides by x - 4

$3 * (x - 4) = \frac{y - 2}{x - 4} * (x - 4)$

$3(x - 4) = {y - 2}$

Open brackets

$3x - 12 = y - 2$

Make y the subject of formula

$3x - 12 + 2= y$

$3x - 10 = y$

Reorder

$y = 3x - 10$

Hence, the equation of a line passing through point (4,2) and perpendicular to AB is $y = 3x - 10$

3 0

3 years ago