Final answer:
The equation y=2x-3 is a linear equation because it fits the form y = a + bx with a y-intercept of -3 and a slope of 2. It can be written in standard form as 2x − y = 3, which makes option b the correct choice.
Step-by-step explanation:
To determine whether y=2x−3 is a linear equation and, if so, how to write it in standard form, we start by understanding the definition of a linear equation. A linear equation is any equation that can be written in the form y = a + bx, where a is the y-intercept, b is the slope, x is the independent variable, and y is the dependent variable. Since the equation y=2x−3 fits this form with a = -3 (the y-intercept) and b = 2 (the slope), we can conclude it is a linear equation. Next, to write this equation in standard form, which is typically Ax + By = C, we rearrange the terms to get the x-term and the y-term on the same side.
Subtracting 2x from both sides, we get −2x + y = −3. Multiplying through by −1 to have the x-term coefficient positive, we end up with 2x − y = 3, which is the standard form. Therefore, the correct option is b. Linear equation: 2x−y=3. A linear equation is an equation that represents a straight line when graphed. The equation y = 2x-3 is a linear equation because it can be written in the form y = mx + b, where m is the slope and b is the y-intercept. So, the equation y = 2x-3 is a linear equation in slope-intercept form, where the slope is 2 and the y-intercept is -3. To write the equation in standard form, we rearrange it to have all the variables on one side and the constants on the other side. So, the equation in standard form is 2x + y = 3.