Solve this system of equations by graphing.

y = 7/6x + 2

y = -5

Slope: a measure of the steepness of a line, as it represents the ratio that compares the vertical change in y-values to the horizontal change in x-values along the line.

Y-intercept: It is the point on the graph of a linear equation where it crosses the y-axis (vertical axis). This is also the point on the graph where the value of x = 0, while its corresponding y-coordinate is the value of b in the slope-intercept form, y = mx + b. Hence, the coordinates of a y-intercept can be represented as follows: (0, b ).

Horizontal line: The linear equation that is expressed in the form, y = b represents a horizontal line with a slope of zero. A horizontal line has a zero slope because it neither rises, nor falls. When we substitute the value of its slope, m = 0, into the slope-intercept form, y = mx + b, it becomes y = b (because multiplying the x-value by 0 results in a product of 0.

Graphing Instructions/Solution:

Given the following systems of linear equations:

[tex]\displaystyle\mathsf{Equation\:1:\quad y\:=\:\frac{7}{6}x\:+\:2 \quad\Rightarrow Slope\:(m)\:=\:\frac{7}{6},\quad y-intercept:(0,\:2)}[/tex]

[tex]\displaystyle\mathsf{Equation\:2:\quad y\:=\:-5 \quad\Rightarrow Slope\:(m)\:=\:0, \:\:\: y-intercept:(0,\:-5)}[/tex]

Step 1: Plot the y-intercepts

In order to solve for the solution to the given systems of linear equations, we must first plot the y-intercepts of both equations.

[tex]\displaystyle\mathsf{Equation\:1:\quad y\:=\:\frac{7}{6}x\:+\:2 \quad\Rightarrow y-intercept:(0,\:2)}[/tex]

[tex]\displaystyle\mathsf{Equation\:2:\quad y\:=\:-5 \quad\Rightarrow\:\: y-intercept:(0,\:-5)}[/tex]

Step 2: Use the slope to plot other points for Equation 1

After plotting the y-intercepts of both equations on the graph, use the slope ("rise over run " technique) to plot other points on the graph. Continue plotting points until we have enough points to connect a line with.

[tex]\displaystyle\mathsf{Equation\:1:\quad y\:=\:\frac{7}{6}x\:+\:2 \quad\Rightarrow Slope\:(m)\:=\:\frac{7}{6} \Rightarrow \:rise\:7\:units,\:run\:6\:\:units\:\:to\:\:the\:\:right }[/tex]

Step 3: Plot other points for Equation 2 using y = -5

Since Equation 2 has a slope, m = 0, then it means that it doesn't have any vertical change. We can plot other points for this equation by using the same y-coordinate, y = -5. Alternatively, we can draw a horizontal line from the y-intercept (0, -5).

[tex]\displaystyle\mathsf{Equation\:2:\quad y\:=\:-5 \quad\Rightarrow Slope\:(m)\:=\:0}[/tex]

Step 4: Find the intersection of points on the graph

The point where the graph of both lines intersect represents the solution to the given system. The solution to the given system occurs at point (-6, -5).

Kindly refer to the attached screenshot of the graphed system where it shows the point of intersection occurring at point (-6, -5).

Keywords:

Slope

Horizontal Line

Y-intercept

Zero slope

Systems of linear equations

Solve by graphing

For more on the subject, refer to the following question: https://brainly.com/question/15362774

Solve this system of equations by graphing. y = 7/6x + 2 y = -5

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