EQUATIONS OF LINE
Answers with Step-by-step explanation:
Before we answer the table, let us have here a brief discussion about the topic. The form Ax + By = C is the standard form of linear equation. On the other hand, the form y = mx + b is referred to as the slope-intercept form. Other books use f(x) = mx + b but f(x) is still the same as y. The values of m and b represent the slope and the y-intercept respectively. The x-intercept can be obtained when y is set to zero. On the other hand, the y-intercept can also be obtained when x is set to zero. The two intercepts: x and y- intercepts, are the points where the graph of the linear function touches the x and y- axes respectively.
1. Standard Form: 2x + 3y = 6
To make it in standard form, just subtract 2x on both side of the equation. The purpose of this is to isolate the term which contains the y variable. The resulting equation is: 3y = -2x + 6. Divide both sides by 3 and we will get its slope-intercept form: y = -2/3 x + 2. So:
Slope-intercept form: f(x) = -2/3 x + 2
Slope: -2/3
x-intercept: 3
y-intercept: 2
2. Standard Form: 3x - y = 4
Slope-intercept form: f(x) = 3x - 4
Slope: 3
x-intercept: 4/3
y-intercept: -4
3. Standard Form: x + 2y = 4
Slope-intercept form: f(x) = -1/2 x + 2
Slope: -1/2
x-intercept: 4
y-intercept: 2
4. Standard Form: 2x - 5y = -15
Slope-intercept form: f(x) = 2/5 x + 3
Slope: 2/5
x-intercept: -15/2
y-intercept: 3
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