Explanation:
To evaluate the proposed, the comprehension of linear data is required,
Slope: The rise/run or the accumulative unit distance between two differentiated points on a linear.
X-intercept: The peculiar point in which the observed linear data intersects the x-axis.
Y-intercept: The peculiar point in which the observed linear data intersects the y-axis.
1. To solve the following systems, first convert the Slope-Intercept formatting to Standard (General) form:
y = -5/3x + 3
3(Y = -5/3x + 3) Product by the denominator to eliminate the fraction.
3y = -5x + 9. Add 5x to the other expression as in standard form, the slope must be positive.
5x + 3y = 9 <== Standard (General) Form.
Y = 1/3x - 3
3(y = 1/3x - 3). Product by the denominator to eliminate the fraction.
3y = x - 9. Subtract by x to place the slope within the other expression of the equation.
-1(-x + 3y = -9). Now, product by -1 to contribute to a positive slope.
X - 3y = 9 <=== Standard (General) Form.
2. To solve for the x and y values, utilize the system of substitution:
1(5x + 3y = 9)Multiply equations by opposite slope to the other, and a positive to other.
-5(X - 3y = 9)
Evaluate,
+ 5x + 3y = 9. Now, add the systems.
-5x + 15y = -45
——————————
18y = -36
Y = -2
Thus, now that y is equated to -2, substitute that to either equation.
X - 3y = 9
X - 3(-2) = 9
X + 6 = 9
X = 3
Thus, x = 3, y = -2. This is their intersection point.
To plot these lines on the graph, execute the following,
Y = -5/3 x + 3
Start with the y-intercept. Draw a point on number 3 on the y-axis (vertical).
Starting with that point, go down 5 units, right 3 units.
* Remember, if there is a negative rise, go down. Positive, go up. If there is a negative run, go left. Positive, go right.
* Keep going 5 units down, right 3 units, until the graph allows.
2. Y = 1/3 x - 3
Similarly, conduct the same steps:
Starting with the y-intercept, draw a point on -3 on the vertical, or y-axis.
Beginning on that point, go up 1 unit, right 3 units.
Keep going up 1 units and 3 units right until the graph permits.
*I hope this helps.