Question

Graph the line with slope of 53 5/3 and goes through the point (2,1).

Answer 1

Answer:

We kindly invite you to see the image attached for further details.

Step-by-step explanation:

From Analytical Geometry we get that linear functions can be found after knowing a point and its slope. The standard form of a linear function is represented by the following formula:

$y =m\cdot x +b$ (Eq. 1)

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

At first we need to calculate the y-Intercept, which is cleared within (Eq. 1):

$b = y-m\cdot x$

If we know that $y = 1$, $x = 2$ and $m = \frac{5}{3}$, then the y-Intercept of the linear function is:

$b = 1-\left(\frac{5}{3} \right)\cdot (2)$

$b = -\frac{7}{3}$

Line with a slope of $\frac{5}{3}$ that goes through the point (2, 1) is represented by $y = \frac{5}{3}\cdot x -\frac{7}{3}$.

Lastly, we graph the line by using a plotting software (i.e. Desmos), whose result is included below as attachment.