Question

What do the following two equations represent? 4x-2y=-5 y=-(1)/(2)x-(1)/(10)

Answer 1

The given equations 4x - 2y = -5 and y = -1/2x - 1/10 represent linear equations in two variables. Equation 1 represents a straight line on a graph, and Equation 2 represents a line with a negative slope.

Step-by-step explanation:

The given equations are:

4x - 2y = -5 (Equation 1)

y = -½x - ½ (Equation 2)

Equation 1 represents a linear equation with two variables, x and y. The equation can be rearranged to solve for y in terms of x or vice versa. It represents a straight line on a graph, where the x-intercept and y-intercept can be determined by setting x or y to zero respectively.

Equation 2 is also a linear equation, which represents a line with a negative slope. The slope is the coefficient of x, which is -½. The y-intercept is the constant term, which is -½.

Answer 2

The equations 4x - 2y = -5 and y = -(1)/(2)x - (1)/(10) are both linear equations representing straight lines on a coordinate plane, with distinct slopes and y-intercepts.

Step-by-step explanation:

The two given equations, 4x - 2y = -5 and y = -(1)/(2)x - (1)/(10), are linear equations. Linear equations represent straight lines when graphed on a coordinate plane. To understand these equations, let's look at each one separately.

The first equation can be rearranged into slope-intercept form (y = mx + b) to make it easier to understand its graph:

• 4x - 2y = -5
• -2y = -4x - 5
• y = 2x + (5/2)

Where the slope (m) is 2 and the y-intercept (b) is 5/2.

The second equation is already in slope-intercept form:

• y = -(1)/(2)x - (1)/(10)

Where the slope is -(1)/(2) and the y-intercept is -(1)/(10).

Graphically, these equations would be represented by two lines on the Cartesian plane, each with their respective slopes and y-intercepts.