1) The standard form of a linear equation is written as .
1 answer:
Answer:
Step-by-step explanation:
The equation of the line, expressed in slope-intercept form is:
Where m the slope and yo the y-intercept.
Since we are given the line in standard form:
ax+by=c
To find the slope-intercept form, we just solve it for y:
Comparing the last equation with the slope-intercept form:
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The graph shows a piecewise function, meaning that different functions are shows at different intervals (ranges of x-values).
1) One of the graphs is part of a parabola, meaning the equation is quadratic (has
). That equation must be 
.
2) The other graph is a straight line, meaning it must be a linear equation. That equation must be x + 4.
Looking at the entire graph, you can see that the parabola starts from the left and ends with an open circle at x=2. An open circle means that the graph doesn't have a value at that point, x=2. The linear line starts with a filled point at x=2 and continues to the right. That means we're looking for the choice where:
1)
Since x=2 cannot be a point in the graph, and less than 2 means that the graph includes everything to the left of 2, but not including 2
2)
Since x=2 is a point in the graph, and greater than or equal to 2 means that the graph includes 2 and everything to the right of it
------
Answer: C)
1) One of the graphs is part of a parabola, meaning the equation is quadratic (has
2) The other graph is a straight line, meaning it must be a linear equation. That equation must be x + 4.
Looking at the entire graph, you can see that the parabola starts from the left and ends with an open circle at x=2. An open circle means that the graph doesn't have a value at that point, x=2. The linear line starts with a filled point at x=2 and continues to the right. That means we're looking for the choice where:
1)
Since x=2 cannot be a point in the graph, and less than 2 means that the graph includes everything to the left of 2, but not including 2
2)
Since x=2 is a point in the graph, and greater than or equal to 2 means that the graph includes 2 and everything to the right of it
------
Answer: C)
Answer:
x= 1.5, y= 3.5
or x= -5, y= 10
Step-by-step explanation:
Let's solve by substitution.
Label the two equations:
y= 2x² +6x -10 -----(1)
y= -x +5 -----(2)
Substitute (2) into (1):
2x² +6x -10= -x +5
2x² +6x +x -10 -5= 0
Simplify:
2x² +7x -15= 0
Factorise:
(2x -3)(x +5)= 0
2x -3= 0 or x +5= 0
2x= 3 or x= -5
x= 1.5
Now that we have found the value of x, we can find the value of y through substitution.
Substitute into (2):
y= -1.5 +5 or y= -(-5) +5
y= 3.5 or y= 10
Supplementary:
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